Development of levitated electromechanics of nanodiamond ...

Development of levitatedelectromechanics of nanodiamond in

a Paul trap

Anas Almuqhim

A dissertation submitted in partial fulfillment

of the requirements for the degree of

Doctor of Philosophy

of

University College London.

Department of Physics and Astronomy

University College London

December 18, 2019

2

I, Anas Almuqhim, confirm that the work presented in this thesis is my own.

Where information has been derived from other sources, I confirm that this has been

indicated in the work.

Abstract

This thesis outlines the development of an experimental platform to explore recent

theoretical proposals to create macroscopic spatial quantum superposition using a

levitated nanodiamond containing nitrogen vacancy centres (NV). The work has

demonstrated a method for electrodynamic levitation of nanodiamond and explored

the feasibility and limitations of this system for experiments in macroscopic quan-

tum mechanics.

A range of electrical trap geometries were explored to determine their suitability

for diamond levitation. A linear quadrupole trap was chosen and two different traps

were designed, constructed and tested at atmospheric pressure and under vacuum.

One trap was of a conventional linear Paul trap design, which was integrated with

a microwave antenna as one of the electrodes for excitation of NV centres in the

nanodiamond. A more cost effective trap was also designed and constructed from a

printed circuit board. This design was easy to fabricate and had a larger numerical

aperture for enhancing signal detection. Although not eventually used in this work

it has found application in other levitation experiments in the laboratory.

Most of the work in this thesis utilises a conventional linear Paul trap with inte-

grated microwave excitation. The magnetic field strength and the energy density

of the microwave field within the trap was modelled and were found to be suitable

for excitation of NV centres. Using this trap we demonstrated optically detected

magnetic resonance (ODMR) of the NV centres of diamond placed in the trap. NV

fluorescence from microdiamond in this system was used to investigate the depen-

dence of NV photoluminesence as a function of temperature, laser power and gas

pressure. It was found that the temperature change not only affected the resonance

Abstract 4

frequency but also the ODMR contrast. The contrast reached its peak at about of

11.7± 0.2 % at 380± 35 K down to 3.2± 0.2 % at 657± 20 K. We demonstrated

the ability to trap 100 nm diamond down to 4×10−3 mbar and observed the NV

photoluminesence at atmospheric pressure.

Impact statement

The principle of superposition is a central part of quantum theory that has been

demonstrated in the microscopic world for particles ranging from electrons all the

way up to very massive molecules containing thousands of atoms. However, it is

still an open question as to whether it is a universal principle that holds for all mass

scales. An answer to this question for even larger systems, such as nanoparticles,

will not only have impact on our knowledge of the universality of quantum me-

chanics but also on the limits of macroscopic quantum technologies that utilise this

principle.

The work outlined in this thesis represents the development of an experimental plat-

form, using levitated nanodiamond, that eventually aims to test the macroscopic

limits of quantum mechanics using matter-wave interferometry. This work has de-

signed, tested and demonstrated methods for electrodynamic levitation of nanodia-

mond, as well as the detection of embedded nitrogen vacancy centres (NVs), both

of which are central to this type of matter-wave interferometry. The trapping of

nanodiamond in vacuum within a Paul trap, may have an impact on the way future

high-mass, matter-wave interferometry experiments can be carried out. In addition,

the work in this thesis has highlighted some significant technical problems, such as

that the internal heating of nanodiamond, must be overcome before nanodiamond

matter-wave interferometry can be realised.

Acknowledgements

First, all praises to Allah for the strength and his blessing in completing this thesis.

I would like also to express my sincere gratitude to my supervisor Professor Peter

Barker for his exceptional support and for patiently offering me guidance and advice

on my research with practical issues that go beyond the textbooks. Without him, this

thesis would not have been possible.

I am also grateful to King Abdulaziz City for Science and Technology (KACST)

for funding my studies at UCL.

Many thanks also to the past and present members of the Barker group, for their

exceptional support and for providing me with an excellent atmosphere to carry out

my research. It would have been a lonely road without them.

I would like to give special thanks to Dr. Sultan Ben Jaber for granting me access

to Raman spectroscopy in the chemistry department at UCL. I would also like to

thank Dr. Khaled Aljaloud for giving me access to CST software in the electrical

engineering department at UCL. I must also thank Dr. Masfer Alkahtani for the NV

diamond samples.

Finally, my deepest gratitude goes to my beloved parents and brothers. They are

always supporting and encouraging me with their best wishes.

Contents

1 Introduction 17

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

1.3 Thesis structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2 The nitrogen vacancy centre in diamond relevant to matter-wave inter-

ferometry 24

2.1 Optical and spin properties . . . . . . . . . . . . . . . . . . . . . . 24

2.2 Electron spin measurement . . . . . . . . . . . . . . . . . . . . . . 26

2.3 Creating a spin superposition . . . . . . . . . . . . . . . . . . . . . 28

2.4 Spin coherence lifetime . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Temperature and pressure dependence . . . . . . . . . . . . . . . . 29

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Paul traps for levitation 32

3.1 Trapping principles . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Linear quadrupole trap . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Secular motion and micromotion . . . . . . . . . . . . . . . . . . . 38

3.4 Pseudopotential approximation . . . . . . . . . . . . . . . . . . . . 40

3.5 Geometrical efficiency factors . . . . . . . . . . . . . . . . . . . . 41

3.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Paul trap design 45

4.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

Contents 8

4.2 Linear quadrupole trap with endcaps . . . . . . . . . . . . . . . . . 45

4.3 Quadrupole trap on printed circuit board . . . . . . . . . . . . . . . 50

4.4 Stylus traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

5 Fabrication, loading and characterisation of the Paul trap 59

5.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Fabrication of implemented designs . . . . . . . . . . . . . . . . . 59

5.2.1 PCB trap . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2.2 Linear quadrupole trap with endcaps . . . . . . . . . . . . . 60

5.3 Loading methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.1 Piezo-speaker . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.3.2 Nebuliser . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.3.3 Electrospray . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4 Characterisation of Paul traps . . . . . . . . . . . . . . . . . . . . . 69

5.4.1 PCB trap . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.4.2 Linear quadrupole trap with endcaps . . . . . . . . . . . . . 71

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6 Microwave excitation of NV diamond 79

6.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

6.2 Different design geometries . . . . . . . . . . . . . . . . . . . . . . 79

6.3 Microwave antenna integrated into the Paul trap . . . . . . . . . . . 83

6.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7 NV photoluminescence with temperature, laser intensity and gas pres-

sure 96

7.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.2 Microwave source . . . . . . . . . . . . . . . . . . . . . . . . . . . 96

7.3 ODMR detection set-up . . . . . . . . . . . . . . . . . . . . . . . . 97

7.4 Experimental set-up . . . . . . . . . . . . . . . . . . . . . . . . . . 99

7.5 Recorded NV spectra . . . . . . . . . . . . . . . . . . . . . . . . . 100

Contents 9

7.6 Optically detected magnetic resonance . . . . . . . . . . . . . . . . 102

7.7 Zeeman splitting of ODMR spectra . . . . . . . . . . . . . . . . . 105

7.8 Photoluminescence as a function of pressure . . . . . . . . . . . . . 108

7.9 ODMR spectrum under different vacuum levels . . . . . . . . . . . 113

7.10 Temperature dependence of ZFS . . . . . . . . . . . . . . . . . . . 119

7.11 ODMR contrast . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.12 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

8 Observing NV photoluminescence in the Paul trap 127

8.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

8.2 Sample characteristics . . . . . . . . . . . . . . . . . . . . . . . . 127

8.3 NV photoluminescence from levitated diamond . . . . . . . . . . . 132

8.4 Background noise . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.5 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

8.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

9 Conclusion and future work 140

9.1 Summary of current work . . . . . . . . . . . . . . . . . . . . . . . 140

9.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

Bibliography 145

List of Figures

1.1 Time evolution of the experimental set up proposed by Bose et al.

A nanodiamond levitated in an optical trap under strong magnetic

field gradient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

1.2 Time evolution of the experimental set up proposed by Bose et al

by dropping the particle. . . . . . . . . . . . . . . . . . . . . . . . 21

2.1 The NV centre in diamond. . . . . . . . . . . . . . . . . . . . . . . 24

2.2 The electronic level structure of the NV centre in diamond. . . . . . 25

2.3 Fluorescence spectra of single NV centre in diamond. . . . . . . . . 26

2.4 ESR spectrum of NV− under different external magnetic field (B)

strengths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.5 NV centre orientations. . . . . . . . . . . . . . . . . . . . . . . . . 28

3.1 A diagram that shows the electrode configuration of two dimen-

sional quadrupole field. . . . . . . . . . . . . . . . . . . . . . . . . 33

3.2 A diagram that shows a four electrode structure of the two dimen-

sional AC field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

3.3 The hyperbolic saddle surface generated by an AC voltage over a

half cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.4 A conventional linear quadrupole trap. . . . . . . . . . . . . . . . . 36

3.5 Stability diagram for the linear Paul trap . . . . . . . . . . . . . . . 38

3.6 Quadrupole equipotential lines for hyperbolic and cylindrical elec-

trodes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

4.1 Linear quadrupole with endcaps. . . . . . . . . . . . . . . . . . . . 46

List of Figures 11

4.2 Opening angle of the linear quadrupole trap. . . . . . . . . . . . . . 47

4.3 Comparison of the calculated potential between the two AC elec-

trodes in the linear quadrupole with endcaps trap. . . . . . . . . . . 47

4.4 Calculated electric field for the quadrupole trap with end-

caps. The AC electrodes are held at 300 V and the end-

caps at 300 V. The separation between the AC electrodes is

3.5 mm and the distance between endcaps in z direction is

11 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.5 Geometry of the PCB trap. The four-rod geometry of the linear

quadrupole trap is changed to a set of plane electrodes to improve

optical accessibility. The electrodes are printed on a dual sided PCB. 52

4.6 Calculated electric field for the PCB trap. The AC and endcaps elec-

trodes are held at 300 V. The separation between the AC electrodes

is 1.6 mm and the distance between endcaps in x direction is 5.8 mm. 53

4.7 A 3D model of the stylus trap with conical electrodes. . . . . . . . . 54

4.8 The electric field for the stylus trap with conical electrodes. The AC

electrodes are held at 300 V and the DC at 0 V. . . . . . . . . . . . 55

4.9 Trap geometry of the styles trap with cylindrical electrodes as de-

scribed by Maiwald et al. . . . . . . . . . . . . . . . . . . . . . . . 56

4.10 Electric field for the stylus trap with cylindrical electrodes. The AC

electrodes are held at 300 V and the GND and DC electrodes at 0 V. 57

5.1 The design layout of the PCB trap printed on transparent paper. . . . 60

5.2 A cross-section of one quadrupole rod. This consists of three main

parts: an AC electrode, a DC electrode and spacers to isolate the two. 60

5.3 A 3D model of the linear quadrupole trap with endcaps. The trap

consist of three main parts: AC electrodes, DC electrodes and spacers. 61

5.4 A photo of the linear quadrupole trap with endcaps. The electrodes

of this trap are made of stainless steel and separated by nylon spac-

ers. Nylon holders were used to hold the trap structure. . . . . . . . 62

5.5 Paschen curve for the ideal case in air. . . . . . . . . . . . . . . . . 65

List of Figures 12

5.6 Paschen curve for the linear Paul trap and the PCB trap. . . . . . . . 65

5.7 A schematic diagram showing the electrospray setup and loading

process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.8 The experimental setup of the PCB trap. . . . . . . . . . . . . . . . 69

5.9 A photograph of 10 µm silica trapped under vacuum in the PCB trap. 70

5.10 An extra slot was milled between the AC and DC electrodes in PCB

trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71

5.11 A 3D model of part of the piezo housing. . . . . . . . . . . . . . . 72

5.12 The experimental setup of the linear quadrupole trap with endcaps. . 72

5.13 A photograph of a 10 µm silica particle trapped at 1.8×10−2 mbar

in the linear quadrupole trap with endcaps. . . . . . . . . . . . . . . 73

5.14 A photograph of a 100 nm diamond trapped at atmospheric pressure

in the linear quadrupole trap with endcaps. . . . . . . . . . . . . . . 75

5.15 The measured trap frequency after trapping 100 nm diamond under

4×10−3 mbar in the linear quadrupole trap. . . . . . . . . . . . . . 77

5.16 Simulated secular frequency in the linear quadrupole trap. . . . . . 78

6.1 3D geometry of the loop antenna. . . . . . . . . . . . . . . . . . . . 81

6.2 Plots of the absolute value of the magnetic field strength contours

created by a loop antenna with 0.5 W of input power. . . . . . . . . 81

6.3 Calculated absolute value of the magnetic field strength for a loop

antenna with an outer diameter of 2 mm and an inner diameter of

1.4 mm. The input power is 0.5 W. . . . . . . . . . . . . . . . . . . 82

6.4 The absolute value of magnetic field strength contours of the

monopole antenna at an input power of 16 W. . . . . . . . . . . . . 84

6.5 The absolute value of magnetic field strength and power density of

a monopole antenna at 16 W input power along x,y and z axes. . . . 85

6.6 Absolute value of the magnetic field strength contours of a

monopole antenna at 16 W input power, after placing a second

grounded electrode. . . . . . . . . . . . . . . . . . . . . . . . . . . 86

List of Figures 13

6.7 Calculated absolute value of magnetic field strength and power den-

sity of a monopole antenna, after placing the second grounded elec-

trode on x,y and z axes. . . . . . . . . . . . . . . . . . . . . . . . . 87

6.8 Absolute value of magnetic field strength contours of a monopole

antenna at 16 W input power, when all quadrupole electrodes are

taken into account . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

6.9 Absolute value of magnetic field strength and power density of the

monopole antenna, after placing all quadrupole electrodes along the

x,y and z axes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

6.10 A comparison of power density along x-axis for all the quadrupole

configurations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.11 Absolute value of the magnetic field strength of a loop antenna

formed from two grounded electrodes of the quadrupole trap with-

out AC electrodes. Input power was 16 W. . . . . . . . . . . . . . . 91

6.12 Absolute value of magnetic field strength and power density of

the loop antenna formed from two grounded electrodes of the

quadrupole trap, without the AC electrodes on x,y and z axes. . . . . 92

6.13 Absolute value of the magnetic field strength of the loop antenna

formed from two grounded electrodes of the quadrupole trap, with

16 W input power. . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.14 Absolute value of magnetic field strength and power density of

the loop antenna formed from two grounded electrodes of the

quadrupole trap along the x, y and z axes. . . . . . . . . . . . . . . 94

7.1 A schematic diagram of the microwave source. . . . . . . . . . . . 97

7.2 A schematic diagram of the ODMR detection set-up. . . . . . . . . 98

7.3 A schematic diagram of the experiment. A microscopic glass slide

was inserted vertically between the trap electrodes. . . . . . . . . . 99

7.4 Photograph of the deposited particles, the pixel density is 4 µm/pixel.100

7.5 Spectrum of NV centre acquired with and without presence of the

microwave field. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

List of Figures 14

7.6 A close-up of NV− zero phonon line (ZPL). . . . . . . . . . . . . . 101

7.7 An ODMR spectrum at 0.47 kW/cm2. . . . . . . . . . . . . . . . . 103

7.8 The ODMR spectrum at laser excitation intensities of 0.47, 3 and

10.2 kW/cm2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

7.9 Zeeman splitting of an ODMR spectrum at 0.47, 3 and 10.2 kW/cm2. 106

7.10 Comparison between the ODMR signal with and without an exter-

nal magnetic field at 3 kW/cm2. . . . . . . . . . . . . . . . . . . . 107

7.11 PL saturation curves at different pressures. . . . . . . . . . . . . . . 108

7.12 A PL spectrum at atmospheric pressure and at 4.5×10−1 mbar. . . 110

7.13 A comparison of two PL spectrum profiles at 4.5×10−1 mbar. . . . 110

7.14 A PL spectrum at 2.2×10−4 mbar. . . . . . . . . . . . . . . . . . . 111

7.15 ODMR spectra at atmospheric pressure with varying laser intensity. 114

7.16 ZFS frequency for various laser intensities, at atmospheric pressure. 115

7.17 ODMR spectra at 4.5×10−1 mbar for different laser intensities. . . 116

7.18 ZFS frequency for various laser intensities at 4.5×10−1 mbar. . . . 117

7.19 ODMR spectra at 2.2×10−4 mbar for different laser intensities. . . 118

7.20 ZFS frequency for various laser intensities at 2.2×10−4 mbar. . . . 119

7.21 Temperature dependence of laser intensity at different pressure levels.121

7.22 Deduced temperature from ZFS at different pressures from a change

in laser intensity. . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

7.23 Comparison of the ZFS frequency and corresponding temperature

from a change in laser intensity at different pressure level. . . . . . 123

7.24 Effect of temperature change on ODMR contrast at atmospheric

pressure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

7.25 Effect of temperature change on ODMR contrast at 4.5×10−1 mbar. 124

7.26 Effect of temperature change on ODMR contrast at 2.2×10−4 mbar. 125

8.1 PL spectra of 1 µm in diameter microdiamond particles from

Columbus Nanoworks deposited on a microscopic glass slide by

a nebuliser. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

8.2 PL spectrum of an empty microscope glass slide. . . . . . . . . . . 129

List of Figures 15

8.3 PL pectrum of 1 µm diameter microdiamond particles from Colum-

bus Nanoworks, deposited on a quartz slide by a nebuliser. . . . . . 129

8.4 PL spectrum of microdiamond particles from Columbus Nanoworks

with a nominal diammeter of 1 µm. The particles, in powder form,

were placed directly on a quartz slide. . . . . . . . . . . . . . . . . 130

8.5 PL spectrum from a 100 nm nanodiamond solution from Adamas

Nanotechnologies delivered as 1 mg/ml slurries in DI water. A sam-

ple (100 µg/100 µl) was drop-cast onto a quartz slide. . . . . . . . . 131

8.6 PL spectrum from 100 nm nanodiamond (from Adamas Nanotech-

nologies) delivered as 1 mg/ml slurries in DI water. A mixture of

these particles and ethanol was nebulised into quartz slid. . . . . . . 131

8.7 Schematic of the levitating experiment set-up . . . . . . . . . . . . 134

8.8 An NV spectrum of a levitated diamond . . . . . . . . . . . . . . . 134

8.9 An NV spectrum of a levitated diamond before and after subtracting

the background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135

8.10 The background spectra obtained from the levitated diamond exper-

iment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.11 PL spectrum of the stainless steel electrodes used for the AC and

endcap electrodes . . . . . . . . . . . . . . . . . . . . . . . . . . . 136

8.12 PL spectrum of the nylon spacer. . . . . . . . . . . . . . . . . . . . 137

8.13 PL spectra for various type of glass, using a 532 nm laser. . . . . . . 138

9.1 Schematic of a segment linear quadrupole trap reported by Benson

et al. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

List of Tables

4.1 Geometry efficiency factors for the linear quadrupole trap with end-

caps. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2 Geometry efficiency factors for a PCB trap. . . . . . . . . . . . . . 51

5.1 Operating parameters for trapping 10 µm silica under vacuum in a

PCB trap. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2 Operating parameters for trapping 10 µm and 2.5 µm silica parti-

cles in the linear quadrupole trap. . . . . . . . . . . . . . . . . . . . 74

5.3 Operating parameters for trapping 100 nm diamond at atmospheric

pressure in the linear quadrupole trap. . . . . . . . . . . . . . . . . 74

5.4 Operating parameters for trapping 100 nm diamond at 4× 10−3

mbar in the linear quadrupole trap. . . . . . . . . . . . . . . . . . . 76

7.1 ZFS frequency and ODMR contrast obtained from ODMR spectra. . 103

7.2 Frequency resonances and ODMR contrast obtained from split

ODMR spectra. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

7.3 Coefficients in the polynomial fit for the saturation curves in Fig 7.11.112

7.4 Variation of the photoluminescence intensity with the laser intensity

at different pressure levels. . . . . . . . . . . . . . . . . . . . . . . 112

7.5 ZFS frequency and ODMR contrast obtained from Fig 7.15. . . . . 115

7.6 ZFS frequency and ODMR contrast obtained from Fig 7.17. . . . . 117

7.7 ZFS frequency and ODMR contrast data from Fig 7.19. . . . . . . . 118

7.8 Coupling parameters between temperature and laser intensity. . . . . 121

Chapter 1

Introduction

1.1 Background

Testing the limits of quantum mechanics in the macroscopic domain is currently

of significant interest in physics. More specifically, is quantum mechanics limited

by scale? In its formalism, conventional quantum mechanics does not show any

limitation on mass. The linearity of the Schrodinger equation shows that quantum

superposition states should exist at all scales. This is true in the microscopic regime

as demonstrated for light by Thomas Young in 1801 in his famous double slit ex-

periment and for electrons by Davisson and Germer [1]. However, whether the

superposition principle holds for much larger masses is an open question.

A range of theories have been posited for the rapid collapse of the wavefunction

which would prevent the creation of a superposition on macroscopic mass and

length scales. These include the model by Ghirardi-Rimini-Weber (GRW) [2] which

modifies the Schrodinger equation by introducing nonlinearity and stochastic terms

that scale with mass and size. The Continuous Spontaneous Localization (CSL)

model, which is derived from this work, has been used to predict collapse rates and

has been compared with existing microscopic and macroscopic experiments [3].

Although these models predict collapse, they are phenomenological, and therefore

do not provide a physical mechanism for the process of collapse. However, it is

possible that gravitational interaction with a superposition could lead to wavefunc-

tion collapse and localisation, and this has been initially explored by Penrose and

18

Diosi [4, 5]. Experimental technology is now bringing these theories into the realm

of testability, in which conventional decoherence processes, which would also lead

to collapse, are minimised or controlled. Recent proposals include the use of matter-

wave interferometry [6–10] and optomechanical techniques [11–16].

In 1999, Arndt et al. [17] reported remarkable results proving the de Broglie hypoth-

esis for large objects using C60 fullerene. The particle with highest mass reported

to date in a quantum superposition consists of 104 amu and is an organofluorine

molecule [18, 19]. Since then, however, experimental technology for matter-wave

interferometry has been the barrier to performing these type of experiments for

larger objects. For example, decoherence such as black body emission and absorp-

tion of thermal photons, scattering of light from optical gratings, and collisions with

residual gas molecules, are sources of decoherence that must be controlled. When

silicon particles of 107 amu are diffracted by an optical grating, the scattering of

photons from the grating leads to a reduction in fringe visibility by approximately

10 % [19]. Of experimental importance, it is challenging to have a monochromatic

source of particles which have a narrow enough mass and velocity range such that

the interference pattern is not smeared out through interference with a wide range

of de Broglie wavelengths. Finally, as the particles have such a small de Broglie

wavelength the interference pattern is increasingly difficult to resolve with conven-

tional detectors [18–20].

A different approach to matter-wave interferometry of macroscopic particles was

proposed by Bose et al. [21]. This is a type of Ramsey interferometry that uses

levitated mesoscopic nanodiamond containing singlet spin (S = 1) nitrogen vacancy

centres (NV). This scheme is attractive because it may offer a way of increasing

the mass range up to 109 amu. In this approach a spatial superposition is created

within a trap by using a single NV spin embedded in a larger nanodiamond parti-

cle. In principle this can be a single spin embedded in a macroscopic particle, but

in the interests of concreteness we will adopt the proposal as described in refer-

ences [21, 22]. In this proposal, the atomic spin S = 1 of the NV centre is coupled

to the centre-of-mass motion of the nanodiamond using a magnetic field gradient.

19

An outline of the experiment, and how the interferometer works, is described in

Fig 1.1.

B

B

MW pulse

B

B

t

0 +1 −1

z-axis

mg

Figure 1.1: Time evolution of the experimental set up proposed by Bose et al. [21]. Ananodiamond levitated in an optical trap under strong magnetic field gradientoriented along the z axis. To begin with, the NV diamond centre is initial-ized |Ψ(0)〉 = |β 〉|0〉, and then a microwave (MW) pulse is applied to createa superposition state with equal probability |0〉 → 1√

2(|+ 1〉+ | − 1〉), which

oscillate in opposite directions. By tilting the experiment, a gravitational phaseshift (due to a difference in height) will occur between the two spin states|Ψspin〉 = 1√

2(|+ 1〉+ ei∆φ | − 1〉), which will be measured at the end of the

interferometer. At the end, another MW pulse is sent to measure the spin1√2(|+1〉+ |−1〉)→ |0〉 and perform the Ramsey measurement.

Here a single NV centre inside the nanodiamond is levitated in an optical trap un-

der ultrahigh vacuum to isolate it from the environment. The diamond’s centre-

of-mass motion is in a coherent state |β 〉 and the internal spin state is |Sz〉 = 0

such that the wavefunction is initially governed by |Ψ(0)〉= |β 〉|0〉. At time t = 0,

and under a strong magnetic field gradient oriented in the z-direction, a microwave

pulse is applied to create a spin superposition state of |+ 1〉 and |− 1〉 with equal

probability, |0〉 → 1√2(|+ 1〉+ | − 1〉). The individual spins states of the superpo-

sition are displaced by the field gradient and each oscillates in different harmonic

potentials. At t = T (T equal to the period of oscillation), and by tilting the ex-

periment, a gravitational phase shift (due to a difference in height) occurs between

the two spin states. This introduces a relative phase, due to gravity, between the

spin states |Ψspin〉 = 1√2(|+ 1〉+ ei∆φ | − 1〉), where the phase shift ∆φ = −12λ∆λ

h2ωzT

,

∆λ = 12mgcos(θ)

√h

2mωzand λ = 3µ0mzz0

4π|z0|5gNVµB

√h

2mωz. Here, ωz is the trapping

20

frequency in the z axis, mz is the dipole moment of the static magnetic field along

the z-axis generated by a magnet located at z0, and µ0 is the permeability of vac-

uum. µB denotes the Bohr magneton, gNV the Lande factor and h is the reduced

Planck constant. Finally, another MW pulse is used to measure the probability of

the |+1〉 and |−1〉 to return to the |0〉 state, such that 1√2(|+1〉+ei∆φ |−1〉)→ |0〉.

This experiment has advantages over conventional interferometry, in that it does

not require ground state cooling - although it does require some cooling to retain

the linear regime of the harmonic potential well [21–24]. Additionally, it can, in

principle, use the same trapped particle for many trials of the same experiment. In

this scheme, the spatial separation is only ∼ 1 pm for 100 nm particle using a mag-

netic field of ∼ 1× 104 T/m. This is, therefore, a weak superposition, though it is

enough to verify the creation of a superposition.

A follow up work from Bose et al. [22] demonstrated the ability to create larger

spatial separations up to 100 nm (the size of the particle), by allowing the particle

to free fall. This process is described in Fig 1.2. At time t0 and under a strong mag-

netic field gradient oriented along the z-axis, the optical trap is turned off. A free

falling particle under gravity is in a spin state |β 〉 (|+1〉+|−1〉)√2

. The two spin states

accelerate in opposite directions under the inhomogeneous magnetic field (as in the

Stern Gerlach effect). At t1, a MW pulse is applied to flip the spin, causing the

states to decelerate then accelerate towards each other. At t2, another MW pulse is

applied to slow the spin states so the two components overlap at t3. At t3, a third

MW pulse is sent to close the interferometer; an overall phase which affects one

side of the interferometry arms more than the other will result in a modulation that

indicates the up and down of the interference, as above.

Comparing the two previous schemes proposed by Bose et al., the first scheme has

the advantage of repeating the interference since the particle stays always in the

harmonic well of the trap. However, the free falling scheme offers larger superpo-

sition. It requires an initial feedback cooling and the superposition state is detected

by repeated measurements.

21

𝑩

mg

z-axis

z1

+a

t

+a

-a

-a

-a -a

+a

+a

t0

t1

t2

t3 Detector

𝛽 +1 + −1

2

+1 −1 MW pulse

Figure 1.2: Time evolution of the experimental set up proposed by Bose et al [22] by drop-ping the particle. At t0, the optical trap is turned off, and the particle falls undergravity which is in spin state β

(|+1〉+|−1〉)√2

. The two spin states accelerate in op-posite directions under the inhomogeneous magnetic field. At t1, a MW pulseflips the spin, causing the two spin states start to decelerate, then come to a turn-ing point where they accelerate again. At t2, another MW pulse is used to slowthe two components before they overlap at t3. At t3, a third MW pulse is used toclose the interferometer and carry out the Ramsey interference measurement.

22

1.2 Motivation

To carry out these proposals experimentally, many experimental difficulties must

be addressed. These include the requirement to levitate the nanodiamond under

vacuum to prevent environmental decoherence. In addition, we must be able to ma-

nipulate the spin and then measure the spin state at the end of the protocol. The spin

coherence lifetime must be considerably longer than the trap frequency. A typical

value for NV centres in nanodiamond is 100 microseconds and milliseconds for mi-

crodiamond [25–27]. This implies the trap frequencies must be well in excess of 1

kHz.

There is currently considerable research being undertaken to investigate the viability

of levitating NV diamond particles for matter-wave interferometry [23, 24, 28, 29].

For example, levitation in vacuum by an optical tweezer using 1550 nm or 1064 nm

laser beam has been demonstrated [23, 24, 29]. A 532 nm green laser was used to

initialise the spin, but this, as well as the trapping laser, unfortunately causes heat-

ing of the levitated NV diamond. The resulting increased temperatures increases

the probability of a non-radiative transition. This reduces the effectiveness of the

initial spin polarization required to start the interferometry, and also reduces the

fluorescence from the NV centre which is used to evidence the spatial superposi-

tion [23, 29]. To overcome this problem, the optical trap can be replaced by an

electrical one.

Benson et al. [30] demonstrated the trapping of micron-sized NV diamond in a

linear Paul trap under moderate vacuum conditions, and observed NV fluorescence.

Delord et al. [31] reported the observation of NV fluorescence from 10 µm diamond

at 2× 10−2 mbar. However, the 532 nm excitation laser at 700 µW was powerful

enough to heat up the particle which led to trap loss. This is due the impurities of

the NV diamond sample used. This could be addressed by using purer samples.

This PhD thesis outlines the development of a new experimental platform to explore

the aforementioned recent theoretical proposals [21, 22] to create macroscopic spa-

tial superposition using levitated nanodiamond, containing NV.

23

1.3 Thesis structureThe structure of this thesis is as follows:

• Chapter 2: An outline of the properties of the nitrogen vacancy centre in

diamond, relevant for its use in matter-wave interferometry.

• Chapter 3: A description of the trapping principles of Paul traps, and design

considerations for trapping nanoparticles.

• Chapter 4: The design and modelling of trap geometries suitable for nanopar-

ticle levitation.

• Chapter 5: A description of the fabrication, loading and characterisation of

Paul traps. This includes the production and evaluation of two of the traps

outlined in chapter 4.

• Chapter 6: The design and modelling of in-trap microwave excitation of NV

centres.

• Chapter 7: A study of the photoluminescence of NV diamond from micron-

sized diamond as a function of temperature, laser intensity and gas pressure.

• Chapter 8: A description of levitated nanodiamond experiments in a Paul trap.

• Chapter 9: Conclusion and future research.

Chapter 2

The nitrogen vacancy centre in diamond

relevant to matter-wave interferometry

2.1 Optical and spin propertiesThe nitrogen vacancy centre (NV) in diamond has remarkable properties, such as a

robust spin coherence lifetime and the ability to perform electron spin manipulation

at room temperature. The defect centre of a diamond lattice consists of a nitrogen

atom bonded to three carbon atoms and connected to a local vacancy, as shown in

Fig 2.1.

N C

CC

VC

CC

Figure 2.1: The NV centre in diamond. This consists of one nitrogen atom and three carbonatoms surrounding a central vacancy, trapped in the diamond crystal lattice.

The ground state of the NV has a singlet electron spin (S=1), with spin states

ms = -1, 0, 1 as shown in Fig 2.2. The ms = ±1 levels are offset from the ground

state by 2.87 GHz without an applied magnetic field because of spin-spin interac-

25

tions [32]. This is known as Zero Field Splitting (ZFS). In the |3E,ms = 0〉 excited

state these levels are offset by 1.42 GHz [33].

+ 1

− 1

0

+ 1

− 1

0

MW2.87 GHz

≈ 630-800 nm ISCGreen Light

510 - 540 nm

Ground state

Exited state

Orbital Spin

Excite

High probability

Low

probability

3𝐸

3𝐴2

Red

Fluorescence

637 nm

+ 1

− 1

2𝛾𝐵

Magnetic field

Figure 2.2: The electronic level structure of the NV centre in diamond. The |3A2〉 groundstate and the |3E〉 excited state has three spin states: ms = -1, 0, 1. The tran-sition between these two states is spin conserving. The |3A2,ms = ±1〉 statesare offset from the |3A2,ms = 0〉 state by D = 2.87 GHz, known as Zero FieldSplitting (ZFS). The excited state is populated from the ground state by opticalexcitation using green light (wavelength between 510-540 nm). Electrons inthe |3E,ms = 0〉 excited state decays to the |3A2,ms = 0〉 ground state throughtwo channels. A higher probability transition is observed as 637 nm red fluo-rescence, and lower probability transition via intersystem crossing (ISC). Forelectrons in the |3E,ms = ±1〉 state, decay occurs with higher probability tothe |3A2,ms = 0〉 ground state through the ISC, and with lower probability tothe |3A2,ms =±1〉 ground states. The emission spectrum is approximately be-tween 630 and 800 nm.

Electronic transitions from the |3A2,ms = 0〉 ground state to the |3E,ms = 0〉 ex-

cited state occur by optical excitation using light in the green part of the spectrum,

from 510 nm - 540 nm [34]. The electron then decays to the ground state via two

channels from the |3E,ms = 0〉 state.

The first, fast transition, with higher probability, occurs through radiative decay

with an energy of 1.945 eV. This is observed as red light at 637 nm, and is known

as the Zero Phonon Line (ZPL) of the NV− state, which is the intrinsic energy

difference between the lowest phonon energy level of the |3E〉 and |3A2〉 states.

26

The second, lower probability, transition is through a non-radiative process (also

known as a dark state) via intersystem crossing (ISC) [33,35]. This state was found

to be the neutral charge state (NV0) by Waldherr et al. [36], and this was verified

by Aslam et al. [34]. The NV0 state has a photoluminescence spectrum centred at

610 nm and a ZPL at 575 nm.

A 532 nm laser is commonly used for optical excitation in experiments.

The photoluminescence spectrum is usually acquired between 630 nm to

800 nm to cover the vibrational side bands that extend from the ZPL at

638 nm of the NV− state [33]. This spectrum is normally centred at 680 nm as

shown in Fig 2.3.

Figure 2.3: Fluorescence spectra of single NV centre in diamond showing the 532 nm op-tical excitation laser, the ZPL of NV0 at 575 nm and NV− at 638 nm with theirphonon side bands, adapted from reference [33].

2.2 Electron spin measurement

State preparation of the spin for the proposed matter-wave interferometry experi-

ments requires manipulation of the ground state spin states of the NV centre. The

most straight-forward approach to this is to perform what is commonly known as

electron spin resonance (ESR) measurements (also called electron paramagnetic

resonance EPR) [37]. This is done by tuning a microwave field across the ESR res-

onance, which, in diamond, is at 2.87 GHz for the NV− colour centre in diamond.

27

This will lead to a transition from the |3A2,ms = 0〉 state to the |3A2,ms =±1〉 state.

This transition is observed as a reduction of the photoluminescence count and as a

dip in the recorded ESR spectrum, as shown in Fig 2.4. This process is known as

optically detected magnetic resonance (ODMR).

By applying an external magnetic field (B), the spin ms = ±1 degeneracy will be

lifted by the Zeeman effect with a splitting of 2γB, where γ , the electron gyro-

magnetic ratio, is 2.8 GHz/T. This splitting is detected as two dips in the ODMR

spectrum as shown in Fig 2.4. The frequency separation between the peaks can be

correlated to the strength of the applied magnetic field [33, 35].

Figure 2.4: ESR spectrum of NV− under different external magnetic field (B) strengths.The frequency separation between the peaks can be correlated to the strengthof the applied magnetic field, adapted from reference [38].

In general, NV centres can be found in four different orientations [111], [111], [111]

and [111] within the nanodiamond crystal (see Fig 2.5) which are observed as 8 dips

in an ODMR spectrum [39–42]. The spectral separation between ms =±1 states is

a function of the alignment of the magnetic field with the NV orientations [39–42].

For one NV centre, we expect to observe two dips if the magnetic field is parallel to

the NV axis. For an ensemble, we expect to observe from 2 to 8 dips, depending on

the orientation of NV’s within the sample and the their alignment with the magnetic

28

field [39–42]. For example, Fukui et al. [39] reported the observation of two dips

in the ODMR spectrum for an ensemble, arguing that the magnetic field is parallel

to the [111] direction, and the 10 NV’s within the sample have a [111] orientation.

In a matter-wave interferometry experiment, the NV spin axes should be confined

during the preparation of the spin superposition state, and any rotational motion of

the trapped particle in the axial direction of the ion trap must be avoided. That could

be done by depositing a magnetic material on the NV diamond and use magnetic

field to align the particle [43].

NV V

NN

V

N

V

y

x

z

𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏 𝟏𝟏

Figure 2.5: NV centre orientations. NV axis can be found parallel to [111], [111], [111] or[111].

2.3 Creating a spin superposition

A superposition of the |ms = ±1〉, required for matter-wave interferometry as de-

scribed in chapter 1, can be created in the presence of a magnetic field by applying

two microwave pulses. Initially, green light is used to spin polarise the sample such

that the NV centre is in the |ms = 0〉 state. Following this, a microwave field pro-

vides a resonant π/2 pulse such that 50% of the population in the |ms = 0〉 state

is transferred to the |ms = −1〉 state. Another microwave π pulse is applied that

promotes the remaining population of the |ms = 0〉 state to the |ms =+1〉 state.

For single NV centre there now exists a superposition of | < ψ|ms = −1 > |2 =

|< ψ|ms =+1 > |2 = 12 . The relative phase of this superposition can be set by the

relative phases of the microwave fields [44].

29

2.4 Spin coherence lifetime

Although we have described how the spin superposition can be created, it is im-

portant to understand how the environment effects experiments with NV centres.

Particularly important is the spin coherence lifetime as this sets the timeframe over

which any experiment can be undertaken. Here we have two channels of spin relax-

ation: spin-lattice relaxation time T1 (also called longitudinal relaxation), which is

the transition time between |ms = 0〉, and |ms = ±1〉 and spin-spin relaxation time

T2 (also called transverse relaxation), which is the spin decoherence time [33,45]. In

bulk diamond, T1 is in the range of milliseconds at room temperature, and seconds

up to a few minutes at low temperature [46,47], while T2 is of the order of microsec-

onds at room temperature [25]. In nanodiamond, the value of T1 is in the range of

several microseconds, while T2 is in the range of hundreds of nanoseconds [45].

These values can be increased by decreasing the concentration of embedded NV

centres to prevent any spin-spin interaction between NV’s [48]. The lifetime for the

spatial separation of the ms =±1 superposition states is governed by the T2 time.

2.5 Temperature and pressure dependence

An important consideration for any experiment with NV centres is how temperature

affects the spectroscopy and the spin coherence lifetime. It is possible to use the

zero field splitting (ZFS); the NV centre spin resonance frequencies; for thermom-

etry [33, 49]. As described in section 2.1, the ZFS is the energy difference between

the ms =±1 state and the ms = 0 state, and it is given by D=2.87 GHz for the ground

state, where D is denoted as the ZFS parameter. Firstly, the temperature changes

affect the ODMR spectrum. This is seen as a shift in the ZFS and a reduction in

the PL intensity. This shift in ZFS is explained by local thermal expansion [49,50].

This explanation has been questioned, as it was limited to studies of just the ther-

mal expansion effect [35], though Doherty et al. [51] have since found that the shift

is associated not only with thermal expansion but also with electron-phonon inter-

actions. However, this explanation also depends on impurities and the size of the

diamond sample. A complete mechanism for this shift remains an open question.

30

Here we will focus on three reported results that are commonly used to define tem-

perature dependence of the ZFS [49, 50, 52]. These results could be categorised in

three temperature regions based on the shift in the ZFS parameter, D. These are

defined as low, middle and high temperature regions.

In the low temperature region from 5.6 K to 295 K, Chen et al. [50] reported the

temperature change in the ZFS parameter denoted as D by a fifth-degree polynomial

taking the form:

D(T ) =5

∑n=0

dnT n, (2.1)

where d0 = 2.87771 GHz, d1 =−4.625×10−6 GHz/K, d2 = 1.067×10−7 GHz/K2,

d3 = −9.325× 10−10 GHz/K3, d4 = 1.739× 10−12 GHz/K4 and d5 = −1.838×

10−15 GHz/K5. The shift in D is about 7 MHz in this temperature range (from

2.877 GHz to 2.870 GHz). In the middle temperature region, between 280 K and

330 K, Acosta et al. [49] reported that D changes linearly with temperature with a

negative slope, where dD/dT =-74.27 Hz/K. In the high temperature region from

300 K to 700 K, Toyli et al. [52] reported that D is described by cubic polynomial

function [23, 52]:

D(T ) = a0 +a1T +a2T 2 +a3T 3 +∆pressure +∆strain, (2.2)

where a0 = (2.8697 ± 0.0009) GHz, a1 = (9.7 ± 0.6) × 10−5 GHz/K,

a2 = (−3.7± 0.1)× 10−7 GHz/K2, a3 = (1.7± 0.1)× 10−10 GHz/K3, ∆strain is

the shift in D due to the local strain, which ranges from 2 to 9 MHz [37] and

∆pressure = 1.5 Hz/mbar is the linear shift in D with pressure [53]. Note that,

reducing the pressure from atmospheric pressure to 2.2× 10−4 mbar leads to a

slight temperature rise from room temperature (about 11 mK), which is negligi-

ble in comparison with the temperature change associated with the total shift in

D and the uncertainty in equation 2.2 which is about ±20 K. In this region, the

shift in D is about -56 MHz (from 2.87 GHz down to 2.814 GHz) with gradient

dD/dT =80 kHz/K at 300 K up to dD/dT =170 kHz/K at 700 K.

31

From this we can see that the ZFS parameter D shifts up from 2.87 GHz when the

temperatures decreases, and vice versa when the temperature increases. Increas-

ing the temperature will also increase the probability of a non-radiative transition

through the singlet state, which is observed as a reduction of the PL intensity and

ODMR contrast [49,50,52]. The resulting increase in temperatures not only reduces

the effectiveness of the initial spin polarization required to start the interferometry

but also reduces the fluorescence from the NV centre, which is used to evidence the

spatial superposition. For example, levitation by optical tweezers using a 1550 nm

or 1064 nm laser beam in vacuum is problematic, mainly as a result of the trapping

laser [23, 24, 29]. Optical traps produce an increase in temperature, due to absorp-

tion of the trapping laser light, and these temperature changes affect the contrast of

the electron spin resonance (ESR) spectrum, the intensity of fluorescence emission

and the sharpness of the ZPL peak, especially when the laser power is high [23,29].

In other words, lower laser power leads to a clearer ESR spectrum and higher pho-

toluminescence emission. Moreover, the background gas acts as a heatsink, so, at

lower pressure, the internal temperature of the levitated beads increases and subse-

quently the nano-beads burn at between 10 mbar and 5 mbar [23,54], depending on

the trapping laser wavelength. To address this issue, the optical trap can be replaced

with an electrical one, and this approach is examined in this thesis.

2.6 ConclusionThis chapter described the properties of the NV centre in diamond which are im-

portant for the proposed matter-wave interferometry experiment. These properties

mean that the experiment will require an optical field to initialise the spin, a mi-

crowave antenna to manipulate the spin, and an optically detected magnetic reso-

nance (ODMR) system to readout the spin. A microwave antenna will be integrated

into a Paul trap, and this will be explored in chapter 6. The ODMR detection system

for the trap will described in chapter 7 and 8. Of particular importance is the shift

in zero field splitting (ZFS), which can be used to reveal the temperature changes

induced by a laser in the trap. This will be described in chapter 7.

Chapter 3

Paul traps for levitation

3.1 Trapping principles

Since Wolfgang Paul introduced ion traps in 1953 [55], they have become a useful

tool for many applications requiring mass selection, or for capturing charged parti-

cles in an isolated environment [56]. There are many different types, with the most

common having cylindrical, hyperbolic and linear electrode geometries. All use an

oscillating electric field that leads to the confinement of a charged particle in all

three spatial dimensions [57].

In order to understand the dynamics of a charged particle inside the Paul trap, we

will start by describing the force that governs the motion of a charged particle inside

the potential of a quadrupole field.

The force on a charged particle is given by [57]:

~F =−Q5φ , (3.1)

where Q is the charge and φ is an electric potential in three dimensional space given

by:

φ = G(Ax2 +By2 +Cz2). (3.2)

Here, G is the field gradient and A, B and C are constants which depend on the

geometry. As the Laplacian52φ = 0, this implies that A + B + C = 0. For example,

by considering a two dimensional quadrupole field where A = -B = 1, then C = 0.

33

The potential φ in equation 3.2 is then given by:

φ = G(x2− y2) =φ0

2r02 (x

2− y2), (3.3)

where φ0 is the applied potential (either AC or DC), and r0 is the distance from

the trap centre to the electrode surface as shown in Fig 3.1. This potential can by

realised by four hyperbolic electrodes with infinite length in the z dimension. How-

ever, cylindrical rods are commonly used for greater optical access and simplicity

in fabrication, as described later in this chapter.

Substituting φ from equation 3.3 in equation 3.1, the force can be written as:

~F =−2Qφ0

2r02 (x x− y y). (3.4)

-

++ +

-

F

F

FF

r0

E

x

y

Figure 3.1: A diagram that shows the electrode configuration of a two dimensionalquadrupole field. The potential inside the field is given by equation 3.3. Apositively charged particle near the trap centre will experience an attractiveforce toward the trap centre in the x direction, and a repulsive force from thetrap centre in the y direction.

Consider a positively charged particle near the trap centre, governed by equation

3.4. This particle will be attracted towards the trap centre in the x direction (the

positive x term in equation 3.4) and repulsed from the trap centre in the y direction

(the negative y term in equation 3.4). The opposite occurs for negatively charge

34

particles. This motion implies that it is impossible to confine a charged particle

in all spatial dimensions using a static electric field. This is known as Earnshaw’s

theorem [58]. However, an oscillating (AC) electric field can be used to obtain a net

confinement in the x and y directions toward the trap centre. Consider the electrodes

shown in Fig 3.2 where the potential is given by:

φ0 = 2(U +V cos(Ωt)). (3.5)

The voltages applied to the electrodes U and V are DC and AC respectively, and Ω

is the angular frequency of the oscillating potential.

Figure 3.2: A diagram that shows a four electrode structure of the Paul trap. The fourelectrodes are connected to an AC potential 2(U +V cos(Ωt)). The top andbottom electrodes are connected to the +(U +V cos(Ωt)) terminal and the rightand left electrodes are connected to the −(U +V cos(Ωt)) terminal.

In order to understand how the AC potential leads to a net confinement of a levitated

particle in the x− y plane, we visualise the electrostatic fields and the potential

using a SIMION simulation program. This program solves the Laplace equation

for a particular electrode geometry using a finite difference method [59, 60]. The

two dimensional AC potential forms an oscillating hyperbolic saddle surface which

is flipped from up to down over a half cycle as shown in Fig 3.3, a and Fig 3.3,

c. Consider a positively charged particle near the centre of the trap. At a certain

time t = 0, this particle will be repulsed from the electrodes with a positive voltage

and attracted toward the negative electrodes (see Fig 3.1 and Fig 3.3, a), but after a

35

half of the oscillation period at t = T/2, the electrode voltage has changed sign and

will now attract the particle as shown in Fig 3.3,c. By using appropriate values for

the potentials U and V with a particular oscillation time, the average force pushes

the particle towards the centre of the trap and the particle will be confined in both

x and y directions [57]. The quadratic potential is produced by hyperbolic shaped

equipotential lines as shown in Fig 3.3, b and Fig 3.3, d.

x

y

Potential

+

(a) The saddle-point potential during the firsthalf of the AC cycle at time t = 0.

x

y

Potential

(b) The equipotential lines at t = 0.

x

yPotential

+

(c) The saddle-point potential after half of theAC cycle at time t = T/2.

x

yPotential

(d) The equipotential lines at t = T/2.

Figure 3.3: The hyperbolic saddle surface generated by AC voltage over a half cycle. Theblue ball represents a positively charged particle. The AC potential forms anoscillating hyperbolic saddle surface. In the first half of the AC cycle, theparticle is confined in the x electrode direction (the positive curvature) and anti-confined in the y direction (the negative curvature). After half of the AC cycle,the saddle surface has flipped and the particle is confined in the y direction andanti-confined in the x direction. The particle will be confined in both x and ydirections at a particular AC frequency, where the flipping rate of the saddlesurface is faster than the time required for the particle to escape. This diagramhas been generated using SIMION, where the positive electrodes are held at+300 V and the negative electrodes at -300 V.

36

3.2 Linear quadrupole trap

The linear Paul trap is an example of the two dimensional quadrupole field described

in the previous section, but with additional DC electrodes for confinement in the

remaining axis. This trap consists of four long rod electrodes: two of them with

an applied AC potential, while the other two are at ground (the AC potential could

also be connected between the opposite pair of electrodes). At each end of these

electrodes are two DC electrodes known as endcaps as shown in Fig 3.4, where z0

is the distance between the endcaps and the trap centre, r0 is the distance from the

trap centre to the electrode surface.

x

y

z

Figure 3.4: A conventional linear quadrupole trap. The trap consists of four parallel rods,two connected to an AC potential, and the other two at ground potential. A setof additional DC electrodes at each end of the AC electrodes are used to formthe endcaps.

The potential in the quadrupole trap can be expressed in terms of the geometrical

parameters of the electrodes and the voltage applied to them [57, 61–63]. This is

given by:

φ =

[V2

cosΩt(

1+x2− y2

r20

)]+

[Uz2

0

(z2− 1

2(x2 + y2))] , (3.6)

where V is an AC voltage applied to the AC electrodes, U is a DC voltage applied

37

to the endcaps, z0 is the distance between the endcaps and the trap centre and, r0

the distance from the trap centre to the electrode surface. This potential can be seen

as the sum of the AC potential (first term) and the endcap potentials (second term).

By putting this potential into equation (3.1), we obtain the equations of motion of a

particle of charge Q and mass m in the quadrupole trap:

x =−Qm

(Vr2

0cosΩt−U

z20

)x, (3.7)

y =Qm

(Vr2

0cosΩt +

Uz2

0

)y, (3.8)

z =−2QUmz2

0z. (3.9)

These can be put into the form of Mathieu equations:

d2udζ 2 +(au−2qu cos(2ζ ))u = 0, (3.10)

where u represent x, y or z, and

ax = ay =−12

az =−4QU

mΩ2z20, (3.11)

qx =−qy =−2QV

mΩ2r20,qz = 0, (3.12)

ζ =Ωt2. (3.13)

These equations have a standard solution within the region of stable trapping for

parameters a and q, and that satisfy the condition |a| << q2 < 1 for the first sta-

bility region as shown in Fig 3.5, b. It should be noted that, in the second stability

region, denoted as regions B and C in Fig 3.5, a, where the value of a and q are

high, the micromotion can be of the same order as the macromotion [64]. Here, a

higher voltage and driving frequency for trapping are required. This motion will be

discussed in the next section.

38

A

B

C

Stability regions

0 1 2 3 4 5 6-4

-2

0

2

4

qu

au

(a) Mathieu stability diagram in two dimensions. The overlap-ping regions between x and y solutions represent the stability re-gions of the trap. The region denoted as A is the first stabilityregion (also known as the lowest stability region) while regionsB and C are the second stability regions.

q = 0.908u

First stability region

0.0 0.2 0.4 0.6 0.8 1.0-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

qu

au

(b) The first stability region (A) near the origin of the Mathieustability diagram. This region represents the commonly operatingregion for the linear Paul trap.

Figure 3.5: Stability diagram for the linear Paul trap in two dimensions. This diagramshows the numerical solution of Mathieu equations. The blue regions representthe x-stable solutions of Mathieu’s equations while the red regions represent they-stable solutions. The diagram shows a symmetry around the au axis. Duringthe experiment, only the positive part of the au axis is considered, though thenegative part could be achieved by swapping the polarity of the trap shown inFig 3.2.

3.3 Secular motion and micromotionThe motion of a charged particle in the trap can be described by Mathieu equa-

tions. The solution of these equation shows a harmonic oscillation with two types

39

of motion: a macromotion (also called a secular motion or trapped motion) and a

micromotion. In order to understand these two motions, we can look at an approxi-

mate solution to Mathieu equations under the condition a,q << 1 [57, 61] where:

u(t) = u0 cos(ωut + τu)(

1+qu

2cosΩt

). (3.14)

The variables u0 and τu determine the initial amplitude and phase respectively, ob-

tained from the initial particle position and velocity, and where the secular motional

frequency is given by:

ωu =Ω

2

√au +

q2u

2. (3.15)

This harmonic motion of a charged particle at frequency ωu and amplitude u0 is

called the macromotion or secular motion. The fast drive frequency Ω applied to

the trap induces motion at that frequency, but with a lower amplitude (related to

the cosΩt term). This motion is superimposed on the secular motion and called the

micromotion. Due to the large contrast between the frequencies of the slow macro-

motin and the fast micromotion (under the condition a,q << 1), the motions can

be seen as two separate motions. However, although this is true in the first stability

region, in higher stability regions the amplitude and frequency of the micromotion

can be of the same order as the secular motion [64]. The charged particle motion

gives the average kinetic energy over one period of the macromotion [61]:

EKu =12

m⟨u2⟩∼= 1

4mu2

0

(ω

2u +

18

q2uΩ

2)

∼=14

mu20ω

2u

(1+

q2u

q2u +2au

)∼=

14

mu20ω

2u︸︷︷︸

macromotion

+14

mu20ω

2u

(q2

uq2

u +2au

)︸︷︷︸

micromotion

.

(3.16)

In the z direction, where qz = 0, the micromotion term in equation 3.16 vanishes((q2

zq2

z+2az

)≈ 0)

and then the total kinetic energy can be described by the macro-

40

motion term. That means the micromotion can be minimized by keeping the particle

near the trap centre (close to the AC null point). In the x and y directions, and un-

der the stability condition |au|<< q2u < 1, the kinetic energy of the micromotion is

equivalent to the kinetic energy of the macromotion, since the expression(

q2u

q2u+2au

)in the micromotion term in equation 3.16 must be almost equal to 1 in order to

satisfy the stability condition. The trapped particle cannot be positioned at the trap

centre at all times, as it will still fluctuate around the saddle point and the micromo-

tion will remain. Assuming a secular motion which is in thermal equilibrium with

a bath of temperature Tx,y,z. From the equipartition of energy, the average value of

the kinetic energy can be written as:

⟨EKz

⟩=

14

m⟨u2

tz

⟩ω

2z =

12

kBTz, (3.17)⟨EKx,y

⟩=

12

m⟨

u2tx,y

⟩ω

2x,y = kBTx,y, (3.18)

where T is the particle temperature, kB is Boltzmann’s constant and⟨u2

t⟩

is the

variance amplitude of the thermal motion. From equation 3.17 and 3.18, we can

see that the energy of the macromotion can be reduced be decreasing⟨u2

t⟩, which

could be achieved by cooling [61, 65].

3.4 Pseudopotential approximationThe AC potential in equation (3.6) could be simplified to a time-independent poten-

tial by using a pseudopotential. This is basically the time averaged potential over

one oscillation cycle (2π/Ω), and is of the form:

ϕpse =14

QmΩ2 E2 =

14

QmΩ2

(|∇ΦAC(x,y,z)|2

). (3.19)

Now, by using equation (3.19), we can rewrite the potential in equation (3.6) as:

φ =

[14

QV 2

mΩ2r40

(x2 + y2)]+[QU

mz20

(z2− 1

2(x2 + y2))] (3.20)

41

Substituting again into equation (3.1) to obtain the equations of motion, we get:

x =−(

Q2V 2

2m2Ω2r40− QU

mz20

)x, (3.21)

y =−(

Q2V 2

2m2Ω2r40− QU

mz20

)y, (3.22)

z =−(

2QUmz2

0

)z. (3.23)

It can be seen from the equation in the z direction, where only the DC voltage is

applied, that the secular frequency is equal to:

ωz =

√2QUmz2

0. (3.24)

In the x and y directions, the secular frequency is given by:

ωx,y =

√Q2V 2

2m2Ω2r40− QU

mz20. (3.25)

It should be noted that, in none of the previous equations, did we account for the

effect of gravity, which shifts the particle from the trap centre. This can be compen-

sated by using a DC offset voltage [66].

3.5 Geometrical efficiency factorsThe equations in the previous sections assume hyperbolic shaped electrodes which

produce a quadratic potential. For non-hyperbolic electrodes, geometrical efficiency

factors are used to account for the non-quadratic potentials which allow the use of

Mathieu equations. Considering a linear Paul trap with cylindrical rods, where the

effect of non-hyperbolic shape electrodes can be written as [67, 68]:

Φ =

[14

QV 2η2

mΩ2r40

(x2 + y2 +σzz2)]+[κQU

mz20

(−εx2 +(1− ε)y2 + z2)] . (3.26)

42

This potential yields secular frequencies given by [68]:

ωx =

√Q2V 2η2

2m2Ω2r40− ε

2κQUmz2

0, (3.27)

ωy =

√Q2V 2η2

2m2Ω2r40− (1− ε)

2κQUmz2

0, (3.28)

ωz =

√Q2V 2η2σz

2m2Ω2r40+

2κQUmz2

0, (3.29)

where η , σz, κ and ε are the geometry efficiency factors [68]. The role of each of

these factors is as follows. The factor η takes into account the effective AC potential

of the electrode shape to the quadratic AC potential in the radial direction, where

( η ≤ 1 ). In the case of an ideal AC potential, η = 1. The factor κ has the same

interpretation as η but for the DC potential in the z direction. The factor σz takes

into account the effect of the residual potential along the z direction from the ap-

plied potential in the x and y directions. This could be negligible, since σz 1 [68].

This factor is equal to zero in the ideal case. The last geometry factor is ε , which

is an anisotropy factor that describes the effect of anisotropy in the DC potential in

the radial direction. The value of the factor ε is equal to 0.5 in the radial symmetric

case [68].

The hyperbolic shaped equipotential lines required for the Paul trap can be tech-

nically achieved using hyperbolic shaped electrodes. Commonly, however, cylin-

drical rods are used, which allow good optical access and simplify the fabrication

process. To get equipotential surfaces that closely approximate hyperbolic elec-

trodes requires that the radius of the electrode be equal to 1.1468 r0 [69] as shown

in Fig 3.6. More recent studies have shown that this number should be between

1.12 r0 to 1.13 r0, where r0 is the distance from the trap centre to the electrode

surface [70–72].

43

(a) Hyperbolic electrodes, r0 = 50 mm. (b) Cylindrical electrodes, r0 = 50 mm.

- 2 5 - 2 0 - 1 5 - 1 0 - 5 0 5 1 0 1 5 2 0 2 51 4 01 6 01 8 02 0 02 2 02 4 02 6 02 8 03 0 03 2 0

Poten

tial (V

)

x ( m m )

(c) The potential between the two x electrodes, where black dots rep-resent the potential for the hyperbolic electrodes and red dots representthe potential for the cylindrical electrodes.

Figure 3.6: Quadrupole equipotential lines for hyperbolic and cylindrical electrodes. Theapplied voltage is 300 V in the opposing x electrodes while the y electrodes aregrounded. The cylindrical electrode diameter is 57 mm. The potential alongthe dashed line in both (a) and (b) is shown in (c). The potential distribution forthe cylindrical electrodes is close to that of the hyperbolic electrode, since theelectrode radius is chosen to be 1.1468 r0. This comparison is modelled usingSIMION.

44

3.6 ConclusionThis chapter is a theoretical description of the dynamics and stability of charged

particles in Paul traps for levitation. This background will be used in the following

chapters to design and examine different trap geometries that are suitable for NV

diamond. For levitated NV diamond, it is important that the traps are as deep as

possible, with a large opening angle between the trap electrodes to collect maxi-

mum light. The quadratic field of an ideal trap suggests a hyperbolic electrode trap

design. However, most traps, including those that described in subsequent chapters,

are not hyperpolic in shape. The geometrical efficiency factors introduced in this

chapter will allow us to take into account the effect of different electrode geometries

introduced in the next chapter. The pseudopotential approximation introduced here

will be used to define and evaluate the depth of these different traps. We can also

use the formalism developed in this chapter to determine the stability criteria of a

particle levitated in such traps.

Chapter 4

Paul trap design

4.1 OverviewThe appropriate trap for our experiment should satisfy two main criteria. Firstly,

the potential well should be as deep as possible to make trapping easier, and to

enable it to hold the particles for long periods. Secondly, a large opening angle (or

numerical aperture) between the trap electrodes is required for efficient detection

of the fluorescence signal from the NV nanodiamond levitated in the trap. Some

established designs that meet these criteria were evaluated and these are described

in the following sections.

4.2 Linear quadrupole trap with endcapsAs described in section 3.2, the linear quadrupole trap consists of four parallel

electrodes that carry AC voltage, as well endcap electrodes with static voltages,

as shown in Fig 3.4. The geometry of this design was chosen to be as close as

possible to the hyperbolic electrode trap. This was achieved by using cylindrical

electrodes with radius R≈ 1.1468r0 and with infinite length. Since the real trap has

a finite length and has endcaps in the z direction, the length of the AC electrodes

was chosen to be twice the gap between the opposing electrodes (4r0). This reduces

the effect of the residual potential along the z direction from the applied potential

in the x and y directions. Considering the length of the AC electrodes, the endcap

electrodes are spaced apart by z0 ≥ 4r0 from the trap centre, with no restrictions on

length and size. In this trap design, shown in Fig 4.1 and Fig 4.2, r0 = 1.75 mm, and

46

each AC electrode has a length of 7 mm (= 4r0) and a radius of 2 mm (= 1.146r0).

The endcaps (DC electrodes) have a 10 mm length and a 2.5 mm in radius. This

trap enables optical access from two directions without any additional modification.

Light is detected through the AC electrodes, which limits the numerical aperture of

this trap to N.A.≈ 0.24 in one direction, as shown in Fig 4.2. Although this is not

a particularly high N.A., we cannot make it higher because we want to maintain

the ideal ratio of the distance between the trap centre and electrode surface to the

electrode radius (≈1.1468), to produce a quadrupole potential close to the ideal hy-

perbolic electrode.

The potential along the x coordinate (the y coordinate should be similar to x due

to radial symmetry) was first investigated using COMSOL Multiphysics. This soft-

ware solves the Laplace equation for a particular electrode geometry using finite

element methods. The result was then compared with SIMION for validation, both

software packages give the same results as seen in Fig 4.3.

x (mm)

y (mm)

z (mm)

Figure 4.1: Linear quadrupole with endcaps. The AC and ground (GND) electrodes havea length of 7 mm and a diameter of 4 mm. The distance between the ACelectrodes is 3.5 mm. The DC electrode length is 10 mm and the diameter5 mm. The AC and DC electrodes are separated by 2 mm.

47

1.75 mm1.75 mm

4 mm

3.7

5 m

m

450

103.807°

31.193°

27.614°

31

.19

3°

NA= 0.24

Figure 4.2: Opening angle of the linear quadrupole trap. The four circles represent the ACelectrodes. The two opposing pair electrodes are separated by 3.5 mm. Theradius of each electrode is 2 mm. The numerical aperture (NA) is about 0.24.

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 51 4 01 6 01 8 02 0 02 2 02 4 02 6 02 8 03 0 03 2 0

Poten

tial (V

)

D i s t a n c e ( m m )

Figure 4.3: Comparison of the calculated potential between the two AC electrodes in thelinear quadrupole with endcaps trap. The applied voltage is 300 V and the sep-aration between AC electrodes is 3.5 mm. The red dots represents the potentialcalculated using COMSOL, the black dots represents the potential calculatedusing SIMION.

48

The electric field distribution has been modelled using COMSOL Multiphysics. The

computed electric field, where both the DC and AC voltage (applied to two of the

AC electrodes; the other two are grounded) is held at 300 V is illustrated in Fig 4.4,

a and Fig 4.4, b, where the colours shows the electric field strength in V/m. The

pseudopotential approximation, which is the time-averaged potential at the secular

frequency, is given by:

ϕpse =14

QmΩ2 E2 =CE2, (4.1)

where C = 14

QmΩ2 , Q and m are the particle charge and mass respectively, Ω is the

driving frequency and E is the electric field strength. This equation shows that the

potential, as seen by any charged particle, is proportional to E2. Here we charac-

terise the trap by the value of E2. Fig 4.4, c is a plot of E2 along the x axis, and

Fig 4.4, d along the z axis. The maximum E2 of this trap is about 3.4×1010 V2/m2

along the x and y axes, and about 4.1×109 V2/m2 along the z axis.

For the matter-wave interferometry experiment, we considered the lowest depth of

the three directions, which represent the energy barrier that a particle must over-

come to escape the trap. We assumed a diamond with a diameter of 100 nm and

one elementary charge, and a driving frequency of 1 kHz. In this case, the depth of

the trap is about 2.3 eV which is equivalent to T= 5.3×104 K.

Two further simulations were carried out in order to calculate the geometry effi-

ciency factors. in the first of these, the AC electrodes were set at 1 volt, and the

endcap DC electrodes grounded, to calculate η and σz. In the second simulation,

the DC electrodes were set at 1 volt, and the AC electrodes grounded, to obtain ε

and κ . These parameters are listed in table 4.1, where we can see that ε is equal

to 0.5 due to the symmetry in the radial coordinate and that the value agree with

that reported by Madsen et al. [68]. Also, the value of σz is 3.24×10−3, so we can

neglect the z2 term in equation 3.20, which was also reported by Madsen et al. [68].

It should be pointed out that η = 0.5 because the voltage is applied at two of the

AC electrodes, whereas the other two were grounded. In case of a voltage applied

to all AC electrodes, this number will be doubled. This value is almost equal to the

49

ideal case (where η=1), because we maintain the distance from the trap centre to

the electrode surface at (≈ 1.1468r0).

(a) Electric field contours in the x-y plane.Colours is used to indicate the electric fieldstrength in V/m. Dark blue circles represent theAC electrodes. The electric field is at a minimumin the trap centre, at point (0,0).

(b) Electric field contours in the z-x plane. Thetwo dark blue rectangles in the centre representthe AC electrodes, while the others are the end-caps. The electric field is at a minimum along theAC electrodes, where particles could be trapped.The field by endcaps will prevent the particlesfrom escaping the trap in the z direction.

- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 0

1

2

3

4

0

1

2

3

E2 x1010

(V/m

)2

x ( m m )(c) E2 along x axis (E2 along y is similar to x).The maximum E2 is about 3.4×1010 V2/m2.

- 4 0 - 2 0 0 2 0 4 00 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 54 . 04 . 5

E2 x109 (V

/m)2

z ( m m )(d) E2 along z coordinate. The maximum E2 isabout 4.1×109 V2/m2. Note that the scale here isdifferent to (a), to recognise the plot shape.

Figure 4.4: Calculated electric field for the quadrupole trap with endcaps. The AC elec-trodes are held at 300 V and the endcaps at 300 V. The separation between theAC electrodes is 3.5 mm and the distance between endcaps in z direction is11 mm.

Table 4.1: Geometry efficiency factors for the linear quadrupole trap with endcaps. For theideal case η = 1, σz = 0, ε = 0.5 and κ = 1.

η σz ε κ

0.5 3.24×10−3 0.5 0.255

50

Overall, this standard design affords a deep trap depth of about 2.3 eV

(T= 5.3× 104 K), and is compact in size, while the opening angle between elec-

trodes is moderate to assure a purely quadratic potential. In addition, as Benson

et al. [30] observed NV fluorescence from microdiamond, using a linear Paul trap

with a N.A. less than 0.2, the N.A. for this trap is sufficient for NV fluorescence

detection.

4.3 Quadrupole trap on printed circuit boardA second trap design was developed and built to improve optical access as com-

pared to the conventional linear quadrupole trap discussed so far. This was made by

deforming the conventional hyperbolic electrodes into a set of planar electrodes on

a Printed Circuit Board (PCB), as shown in Fig 4.5 a and Fig 4.5, b. This approach

was implemented recently in an ion trap [73,74]. The deformation reduced the size

and increased the optical access to the trapped particle.

We first developed a design based on the conventional linear quadrupole trap. This

consisted of four parallel rectangular AC electrodes, each with a length of 4.3 mm

and a width of 2 mm as shown in Fig 4.6, c. A set of four perpendicular rectangular

DC electrodes, with the same dimensions as the AC electrodes, and separated by

2z0 (≈ 5.8 mm), were used for axial confinement. The numerical aperture, when

viewed from the top of the circuit board, is approximately 0.68, as shown in Fig 4.5,

d. This is a significant improvement for fluorescence detection, when compared

with the linear quadrupole trap. However, there is a lack of optical access in the y

direction, as it is blocked by the PCB substrate. This limits the accessibility in this

direction as shown in Fig 4.5, a.

Following the same procedure as that used for the linear quadrupole trap with

endcaps, the electric field is calculated for AC and DC voltages of 300 V, as

shown in Fig 4.6, a and Fig 4.6, b. The maximum E2 for this design is about

3.51× 1010 V2/m2 in the y direction, 1.4× 1010 V2/m2 in the z direction and

1× 1010 V2/m2 in the x direction as shown in Fig 4.6, c and Fig 4.6, d. It can be

seen that, in the radial (y-z) plane, the depth in the y direction is less than that in the

51

z direction. This is because the PCB trap is not as radially symmetric as the linear

quadrupole trap, as the electrodes are much closer to each other in the z direction

(see Fig 4.5). Comparing this trap with the linear quadrupole trap, we find that,

between the AC electrodes in the radial plane, the PCB trap is slightly deeper by

3.2% in one direction and shallower by 59% in the other direction. In terms of the

distance between the endcaps (2z0), the PCB trap is deeper by 144% compared to

the linear quadrupole trap, because the distance between the PCB endcaps is shorter

by 5.2 mm. It is worth mentioning that the PCB trap is only deeper because the

dimensions are smaller compared to the linear quadrupole trap. If the PCB trap had

similar dimensions to the linear quadrupole trap, the potential would be less deep

in all directions. For the matter-wave experiment, the trap depth is about 5.5 ev

(T=13× 104 K) for a charge-to-mass ratio of 0.1 C/kg and a drive frequency of

1 kHz. This means it is deeper by 60.5%, compared to the linear quadrupole trap.

The geometry efficiency factors for this trap are listed in table 4.2. These factors

shows the deviation from the hyperbolic trap. The factor η = 0.35 shows that the

trap depth is reduced by 15 % compared to the ideal case for AC voltage. Here, the

voltage is applied at two of the AC electrodes, whereas the other two are grounded.

In the case of voltage applied to all AC electrodes, this number will be doubled.

This number will be doubled. The factor κ = 0.349 has the same interpretation as

η but for the endcap potential which is reduced by 62 %. It can be seen that the

factor ε is equal to 1.31 due to the asymmetry in the radial (y-z) plane (in the case

of radial symmetry ε = 0.5 as for the linear quadrupole with endcaps). Except for

κ , these factors compare unfavourably to the linear quadrupole trap. However, this

will not affect the trapping principles discussed in the previous chapter, although

the trap depth will be shallower.

Table 4.2: Geometry efficiency factors for a PCB trap [75]. In the ideal case η = 1, σz = 0,ε = 0.5 and κ = 1.

η σz ε κ

0.349 6.2×10−3 1.31 0.382

52

xy

z

(a) A 3D model of the PCB trap. The size of thePCB is 25 mm × 25 mm with a thickness of1.6 mm. Each electrode is labelled with theapplied voltage. The trap includes a slot be-tween the electrodes where the particles shouldbe trapped.

(b) Layout of the PCB trap electrodes without thesubstrate, to show the top and bottom electrodes.This trap consists of four parallel rectangular elec-trodes - two of them with an applied AC potential,and the other two at ground. At each end of theseelectrodes are two perpendicular rectangular DCelectrodes.

Hole (5.8×1.6mm)

Copper (4.3×2mm)

GND

Copper (4.3×2mm)

AC

Top View

x

y

Co

pp

er (

2×4

.3m

m)

DC

Co

pp

er (

2×4

.3m

m)

DC

(c) Top view.The AC and the ground (GND) electrodes have a lengthof 4.3 mm and a width of 2 mm . The DC electrodes have the samedimensions as the AC and ground electrodes. The slot between theelectrodes has a length of 5.8 mm and a width of 1.6 mm. The AC andDC electrodes are separated by 0.75 mm.

PCB substrate (1.6mm)

Copper (70µm) GND

Copper (70µm) AC

Copper (70µm) AC

Copper (70µm) GND

Side View870µm

0.8mm 0.8mm47.4°

85.2°

N.A. = n*sin θ = 0.68

y

z

(d) Side view. Each electrode has a thickness of 70 µm while the thickness of the substrate is1.6 mm. The numerical aperture is about 0.68.

Figure 4.5: Geometry of the PCB trap. The four-rod geometry of the linear quadrupoletrap is changed to a set of plane electrodes to improve optical accessibility. Theelectrodes are printed on a dual sided PCB.

53

(a) Electric field contours in the y-z plane.Colours indicate the electric field strength inV/m. Dark blue lines represent AC and ground(GND) electrodes. The upper right and lower leftelectrodes are AC, while the upper left and thelower right are GND. The electric field is at aminimum in the trap centre, at point (0,0).

(b) Electric field contours in the x-y plane. Thefour white rectangles are the trap electrodes. Thetwo electrodes at x=0 are the AC electrodes,while the other two are the endcaps. The electricfield is at a minimum along the AC electrodes,which represent the trapping area. The field gen-erated by the endcaps will prevent the particlesfrom escaping the trap in the x direction.

- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 54 . 0

E2 x1010

(V/m

)2

D i s t a n c e ( m m )

(c) E2 along x, y and z axes. The red line represents E2 along they axis, the green line represents E2 along the z axis and the blueline represents E2 along the x axis. The maximum E2 is about3.51×1010 V2/m2 on the y axis, 1.4×1010 V2/m2 on the z axisand 1×1010 V2/m2 on the x axis.

Figure 4.6: Calculated electric field for the PCB trap. The AC and endcaps electrodes areheld at 300 V. The separation between the AC electrodes is 1.6 mm and thedistance between endcaps in x direction is 5.8 mm.

To summarise, this trap fulfils the two main criteria mentioned in section 4.1. The

trap shows a depth of about 5.5 ev (T=13×104 K) which is deeper by 60.5% com-

pared to the linear quadrupole trap, while the numerical aperture of this trap is

higher by 183% compared to the linear quadrupole trap. This is a significant im-

provement for fluorescence detection, apart from one direction of optical access

54

along the z-axis. This could be overcome by using a more complicated fabrication

process.

4.4 Stylus trapsThe stylus trap consists of two conical electrodes in a co-axial arrangement. It

has the ultimate optical access with a N.A. = 1, and has also been used to trap

micron-sized graphene particles [76, 77]. An AC voltage is applied to the outer

electrode, while the inner one is held at zero (DC) volts, as shown in Fig 4.7 and

Fig 4.8, a.

Figure 4.7: A 3D model of the stylus trap with conical electrodes in reference [76]. Thistrap consists of two conical electrodes in a coaxial configuration. The innerelectrode is DC electrode while the outer one is the AC. The apex of the innerelectrode is 200 µm higher than the outer electrodes, and the apex angle is 60.The outer electrode is a tapered cone with an upper diameter of 1.6 mm.

In order to examine the suitability of this trap, we have modelled the electric field

distribution using COMSOL Multiphysics. The distribution obtained is shown in

Fig 4.8, a. To determine the depth of the trap when the AC voltage amplitude is

held at 300 V, the trap electrode geometry was obtained from Kane et al. [76] The

E2 distribution shows an axial maximum of about 1.2× 108 V2/m2 and a radial

maximum of about 3.26×108 V2/m2 as shown in Fig 4.8, b and Fig 4.8, c. This is

99.6 % smaller than the linear quadrupole trap with endcaps, due to the non-linear

potential in the axial direction.

For matter-wave experiment, this trap shows a trap depth of about 0.07 eV

(T=0.15×104 K), which is lower by a factor of about 33 than the linear quadrupole

trap.

55

(a) Electric field contours. The dark blue triangle in the mid-dle represents the DC electrode. The right and left trianglesrepresent the cross section of the AC electrode.

2 0 2 1 2 2 2 3 2 4 2 5 2 6

1

3

0

2

4

E2 x108 (V

/m)2

A x i a l c o o r d i n a t e ( m m )(b) E2 in the axial direction. The maximum isabout 1.2×108 V2/m2.

- 1 5 - 5 5 1 5- 2 0 - 1 0 0 1 0 2 00 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 5

E2 x108 (V

/m)2

R a d i a l c o o r d i n a t e ( m m )(c) E2 in the radial direction. The maximum isabout 3.26×108 V2/m2.

Figure 4.8: The electric field for the stylus trap with conical electrodes. The AC electrodesare held at 300 V and the DC at 0 V.

A second design, with similarly high N.A., was also studied to validate the low trap

depth of stylus traps [78, 79]. This design used cylindrical rather than the coni-

cal electrodes, and was surrounded by four cylindrical DC electrodes in a circular

arrangement for radial adjustment and confinement as shown in Fig 4.9.

56

Figure 4.9: Trap geometry of the styles trap with cylindrical electrodes as described byMaiwald et al. [78]. This trap consists of two cylindrical electrodes in a coaxialconfiguration, surrounded by four DC electrodes. The inner electrode is theground (GND) electrode, and the outer one is AC. The AC electrode has aninner radius of 267.5 µm, a thickness of 87.5 µm and a length of 1110 µm.The GND electrode has an inner radius of 50 µm and a thickness of 75 µm. Itis 500 µm higher than the AC electrode. The DC electrodes have a radius of75 µm, and are used to fine-tune the trapping potential generated by the ACand GND electrodes.

Using the same procedure as in the first design, the electric field contours and plots

were determined, and are shown in Fig 4.10. The maximum E2 for this design

is about 3.9× 107 V2/m2 in the axial direction, which is 67.5 % lower than the

previous design. We can conclude that the stylus trap has low trap depth compared

to PCB and linear quadrupole traps. Although it is possible to increase the trap

depth by raising the AC potential, this will increase the possibility of an electric

discharge between the trap electrodes, especially in vacuum, and of reaching the

breakdown voltage described by Paschen’s Law. We will discuss this further in

chapter 5.

57

(a) Electric field contours. The dark blue columns representthe plane cross section of the trap electrodes. The two centralcolumns represent the GND electrode, and adjacent two are theAC electrode which is shorter by 500 µm. The outer columns arethe DC electrodes.

1 . 8 2 . 3 2 . 82 . 0 2 . 5 3 . 00

2

4

6

8

1 0

E2 x107 (V

/m)2

A x i a l c o o r d i n a t e s ( m m )(b) E2 in the axial direction. The maximum isabout 3.9×107 V2/m2

- 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 00

1

2

3

4

E2 x108 (V

/m)2

R a d i a l c o o r d i n a t e ( m m )(c) E2 in the radial direction. The maximum isabout 3.8×108 V2/m2

Figure 4.10: Electric field for the stylus trap with cylindrical electrodes. The AC electrodesare held at 300 V and the GND and DC electrodes at 0 V.

In summary, the stylus trap satisfies only one of the two main criteria discussed in

section 4.1. Although it has a large N.A.(=1), due to a large opening angle, it has a

lower trap depth. As this is an issue that can be overcome by using more conven-

tional designs, we will not consider this trap further for use in these experiments.

58

4.5 ConclusionA range of electrical trap geometries have been modelled to determine their suitabil-

ity for diamond levitation, and for use in the matter-wave interferometry experiment

as described in chapter 1. These geometries included a linear quadrupole trap with

endcaps, a quadrupole trap constructed from a dual-sided circuit board (PCB), and

two stylus trap designs. The designs were chosen and evaluated on the basis of two

main criteria: (a) sufficient trap depth to hold particles for long periods, and (b)

high numerical aperture between trap electrodes for efficient NV fluorescence de-

tection. It was found that while stylus traps have optimum optical access (N.A. = 1),

the depth of this design is about 0.07 ev (T=1500 K) for a charge-to-mass ratio of

0.1 C/kg and a drive frequency of 1 kHz. The linear quadrupole trap and the PCB

trap both have much larger well depths with the same parameters, and the linear

quadrupole trap was approximately 33 times deeper than the stylus trap. The PCB

trap was found to be 2.5 times deeper than the linear quadrupole trap and both traps

had a high enough N.A. for fluorescence detection. The linear quadrupole trap had

an N.A. of 0.24 and the PCB trap had an N.A. of 0.68.

As the stylus trap is significantly shallower than the other traps, it will not be used

for trapping NV diamond. The construction and evaluation of the linear quadrupole

and PCB traps are described in chapter 5.

Chapter 5

Fabrication, loading and

characterisation of the Paul trap

5.1 OverviewIn this chapter we describe the construction and characterisation of the Paul traps,

PCB trap and linear Paul trap outlined in chapter 4. We also describe the particle

loading approaches used in the experiment, and an evaluation of the two traps that

were used.

5.2 Fabrication of implemented designsThe PCB trap and the linear quadrupole trap with endcaps were made to evaluate

their suitability for trapping. These traps were chosen for their deep trap depth and

the fact that they have sufficient N.A. for NV centre fluorescence detection.

5.2.1 PCB trap

The quadrupole trap was printed on a dual-sided PCB. Each side had a 70 µm

copper layer, coated with photoresist film. The fabrication was performed by using

a chemical etching process. The design layout was printed on transparent paper by

using a laser printer (see Fig 5.1), then placed onto the copper layer. Following this,

an ultra-violet lamp was used to transfer the design pattern onto the board using a

photoresist method, creating a mask to protect the desirable conductor. The board

was placed into an acid solution to etch and dissolve excess copper.

60

Figure 5.1: The design layout of the PCB trap printed on transparent paper.

In the region between the electrodes, where the particles should be trapped, a slot

was milled to allow particle loading and trapping.

5.2.2 Linear quadrupole trap with endcaps

The cylindrical rods for this trap are made of stainless steel, where each rod consists

of three main parts as shown in Fig 5.2.

DC electrode Nylon spacerAC electrode

Figure 5.2: A cross-section of one quadrupole rod. This consists of three main parts: anAC electrode, a DC electrode and spacers to isolate the two.

The AC electrodes are cylindrical rods with a length of 61 mm and a diameter of

4 mm. The rods are machined to reduce the diameter to 2 mm leaving the diameter

and length needed for the actual AC electrode in the centre as shown in Fig 5.3, a.

Two tubes of length 10 mm long, inner diameter of 4 mm and outer diameter of

5 mm were placed at each end of the AC electrode to form the DC endcaps

(Fig 5.3, b). The AC and DC electrodes were isolated from each other by two

nylon tube spacers inserted between them. This separated them by 2 mm as shown

in Fig 5.3, c. The final configuration and a photograph of the trap are shown in

Fig 5.3, d and Fig 5.4.

61

(a) AC electrodes. Four AC electrodes are con-structed using 61 mm cylindrical rods with adiameter of 4 mm. Each rod is machined toreduce its diameter to 2 mm over part of itslength, forming an AC electrode with a lengthof 7 mm.

(b) DC electrodes. Four tubes are placed ateach end of the AC electrodes to form the end-caps, each of which has a length of 10 mm, aninner diameter of 4 mm and an outer diameterof 5 mm.

(c) Nylon spacers. Eight nylon spacers areinserted between each AC and DC electrodesto mount the DC eletrode and provide electri-cal insulation. The AC and DC electrodes areseperated by 2 mm.

(d) The complete assembly. The electrodes arecoloured grey, and the red represents the nylonspacers.

Figure 5.3: A 3D model of the linear quadrupole trap with endcaps. The trap consist ofthree main parts: AC electrodes, DC electrodes and spacers.

62

Figure 5.4: A photo of the linear quadrupole trap with endcaps. The electrodes of this trapare made of stainless steel and separated by nylon spacers. Nylon holders wereused to hold the trap structure.

5.3 Loading methodsIt is important for this work that nanoparticles and microparticles are reliably loaded

into the traps. Some dissipation is required to reduce the kinetic energy of the par-

ticles within the trapping region, so that they have an energy lower than the trap

depth. Collisions with gas molecules are used to provide damping as the particles

are launched into the trapping region. In our experiments we have used three dif-

ferent methods to load the particles. These include the use of a piezo-speaker, an

nebuliser and an electrospray, where the particles are initially contained within a

liquid.

5.3.1 Piezo-speaker

A piezo-speaker from Murata Electronics (VSB35EWH0701B) was used to load

particles into the system. This is a ceramic piezoelectric speaker mounted in a

metal ring and driven by a function generator to create a vibrational motion. The

piezo-speaker was placed underneath the trap, located inside a vacuum chamber.

An applied voltage causes the piezo to vibrate at the drive frequency, which drives

63

particles toward the trap centre and overcomes any attractive force that the particles

have with the surface of the speaker.

This attractive force between the particles and the piezo disc is the van der Waals

(VDW) force, and it takes the form (assuming a spherical particle shape) [80–84]:

FVDW = 4πRγs, (5.1)

where γs is the effective solid surface energy and R is the particle radius.

The force generated by the piezo-speaker must be high enough to overcome the

VDW force and launch the particles. The minimum acceleration required to break

the VDW force between the piezo desk and a spherical particle of mass m is there-

fore [80–84]:

a =4πRγs

m=

4πRγs43πR3ρ

∝1

R2 , (5.2)

where m and ρ are the particle mass and density respectively. From this equa-

tion, we can see that the minimum acceleration required to break the VDW force

between the particles and the piezo disc surface increases as the size of the par-

ticles is decreases. For example, for a silica particle, where γs = 0.04 J/m2 and

ρ = 2650 kg/m3, we can calculate that the acceleration is 1.8× 1010 m/s2 for a

100 nm diameter particle, 1.8×108 m/s2 for a 1 µm diameter particle [83, 84], and

1.8×106 m/s2 for 10 µm diameter particle.

The acceleration is limited by the maximum force produced by the piezo-speaker,

which is equal to [81]:

Fpiezo = maap = maApω2p, (5.3)

where Ap and ωp are the piezo oscillation amplitude and its associated frequency

respectively, and ma is the effective mass. The maximum acceleration for the piezo-

speaker used in the experiment is approximately ap = Apω2p = 4.5×107 m/s2. This

64

value indicates the minimum size of silica particle that can be used, which is about

2 µm.

When larger particles of 10 microns are used, they are spread on top of the ceramic

piezo disc before being launched into the trap. For smaller sizes, the particles are

mixed with methanol, then sonicated for an hour in an ultrasonic bath, to avoid

clumping before the solution is decanted onto the piezo disk.

It was found that the particles were projected furthest when the signal generator

was set to sine wave at 20 V and 600 Hz. This is the resonant frequency of this

piezo. Using this piezo-speaker for loading generated a few issues. For example,

we experienced an electrical breakdown between the Paul trap electrodes during the

evacuation of the vacuum chamber. This breakdown occurred when the pressure

was in the tens of mbar range ( depending on the applied voltage between trap elec-

trodes, which was generally around 1 kV in our case). This breakdown is described

by Paschens Law, where the breakdown voltage VB between two electrodes in air is

given by:

VB =bPd

ln(aPd)− ln(ln(1+ γ−1)), (5.4)

where a = 1.125 mbar−1 mm−1, b = 27.375 V mbar−1 mm−1, γ = 0.02 are the

ideal case for air and stainless steel electrodes, P the pressure in mbar and d the

separation distance between the trap electrodes. The graph of equation 5.4 is known

as a Paschen curve and is shown in Fig 5.5. In our case, the Paschen curve for the

linear Paul trap and the PCB trap is shown in Fig 5.6. The minimum breakdown

voltage is about 260 V, which occurs at a pressure of about 3 mbar for the linear

Paul trap and about 6 mbar for the PCB trap.

65

100 101 102 103 104102

103

104

105

106

Pd (mbarmm)

VB(V)

Figure 5.5: Paschen curve for the ideal case in air. VB is the breakdown voltage betweentwo electrodes in air.

100 101 102 103102

103

104

105

106

107

Pressure (mBar)

VB(V

)

Figure 5.6: Paschen curve for the linear Paul trap and the PCB trap. The green line rep-resents the linear quadrupole trap with endcaps, where the separation distancebetween the trap electrodes d=3.5 mm, and the blue line represents the PCBtrap where d=1.6 mm. The minimum breakdown voltage VB is about 260 Vat a pressure of about 3 mbar for the linear quadrupole trap with endcaps andabout 6 mbar for the PCB trap.

The restricted breakdown voltage will be a barrier to applying the right trapping

voltages for high Q/m particles. For this reason, we looked for another approach

to overcoming the voltage breakdown issue, since we must trap at near-vacuum

66

conditions before evacuating to high vacuum. From the Paschen curve in Fig 5.5,

we notice that the breakdown voltage is high at atmospheric pressure and under

pressures of approximately 1 mbar. These two regions are adequate to operate the

Paul trap with a high trapping voltage.

5.3.2 Nebuliser

A nebuliser from Omron (MicroAir NE-U22) was used to load the Paul trap at at-

mospheric pressure, using the method of a passively vibrating mesh [85–87]. A

passively vibrating mesh nebuliser is an ultrasonic probe within the liquid that cre-

ates a strong vibration. This forces the solution containing the particles through the

multiple apertures of the mesh, each with a diameter of 3 µm.

The particles used in our experiment were delivered in a powder form or in 1 mg/ml

slurries in deionised water. Particles in powder form were mixed with methanol or

ethanol, then sonicated for an hour in an ultrasonic bath to avoid any aggregation of

the particles before decanting the solution into the nebuliser container. For particle

slurries in deionized (DI) water, droplets of slurry were mixed with methanol or

ethanol, and then sonicated in the same way as the powder solution.

It should be noted that the nebuliser performs inefficiently (i.e. at a low flow rate)

when particles are in acetone instead of methanol or ethanol. This could be a result

of clogging of the mesh holes due to fast evaporation of the solvent, causing subse-

quent particle aggregation.

Compared to the piezo-speaker described in the previous section, particles can be

trapped with a high trapping voltage at atmospheric pressure, before evacuating the

vacuum chamber to high vacuum. However, it is difficult to vary the trapping volt-

age under the breakdown voltage, while reducing pressure, without breaking the

stability condition for trapping.

5.3.3 Electrospray

A new method of loading was needed in order to prevent any clumping, and pro-

duce highly charged particles, while also being able to load the trap under vacuum

conditions. It was decided that an electrospray system was required for this as this,

67

although the piezo-speaker and the nebuliser were adequate for loading particles

(though not at Ultra High Vacuum (UHV) levels), the particles were not sufficiently

charged and occasionally clumped together. Electrospray works by forcing the liq-

uid that contains the particles through a hollow needle which is maintained at high

voltage. This high voltage produces a strong electric field that causes the solu-

tion droplets to break up (via strong Coulomb forces) and form a fine aerosol. The

droplet size is then further reduced to a steam of single highly charged nanoparticles.

A commercial electrospray deposition system (LV2 from MOLECULARSPRAY)

was used for loading particles under vacuum. This system as seen in Fig 5.7 con-

sisted of an electrospray emitter tip with a 100 µm diameter followed by a 0.25 mm

diameter capillary. A differential aperture was created using a 0.4 mm skimmer

cone and an exit flange. A PEEK microtee was then used to feed the solution from

a syringe tube to the emitter tip passing through a high voltage pin. The particle

solution was prepared using the same process as in nebuliser loading. This solution

was then decanted into the syringe barrel and delivered to the electrospray emitter

by gently pushing the syringe plunger. A high DC voltage with positive polarity

was applied directly to the solution through the microtee. The voltage was then

increased until a sustainable plume was created. This occurred at a voltage of ap-

proximately +3.5 kV, with about 2 mm separation between the emitter tip and the

entrance capillary.

The vacuum system has single stage pumping which used a scroll pump to reduce

pressure from atmospheric down to 1×10−1 mbar. The particles were guided to the

Paul trap by the differential pressure between this stage and the rest of the vacuum

chamber (which was about 1×10−3 mbar).

68

Paul Trap

+3.5 kV

Entrance capillary

Emittertip

Syringe

Gate valve

ScrollPump

P = 1X10-3

mbar

Skimmer

P = 1X10-1

mbar

Plume

Figure 5.7: A schematic diagram showing the electrospray setup and loading process. Anelectrospray deposition system (LV2 from MOLECULARSPRAY) was usedfor loading particles under vacuum. This system consisted of an electrosprayemitter tip with 100 µm inner diameter, an entrance capillary with a diameterof 0.25 mm and a 0.4 mm skimmer cone followed by an exit flange. This alsoacted as a differential pumping aperture. The solution delivery system con-sisted of a syringe with 1 mm diameter PEEK tubing and a PEEK microtee thatjoined the solution to the emitter via a high voltage pin. This high voltage pro-duces a strong electric field that disperses the solution to a fine aerosol, whichwas observed as a sustainable plume. The suction created by the differentialpressure pumping between the first pumping stage and the rest of the vacuumchamber guides the particles toward the Paul trap (from 1× 10−1 mbar at thefirst stage up to about 1× 10−3 mbar at the vacuum chamber). The inset is aphotograph of the electrospray plume.

69

5.4 Characterisation of Paul traps

5.4.1 PCB trap

5.4.1.1 Experimental set-up

The experimental scheme with a photograph of the final set-up is shown in Fig 5.8.

The particles are launched by the piezo-speaker; then pass through a skimmer,

which is a copper-less circuit board with a 1 mm hole in its centre, before finally be-

ing captured by the trap. The trapped particle is illuminated using a diode pumped

solid state laser (Verdi V10 from COHERENT) with a maximum output power of

10 W at 532 nm. The laser beam was coupled to an optical fibre using two mirrors

and a collimator, and the other end of the optical fibre was embedded within the

PCB through a 0.3 mm hole drilled from the board side toward the trap centre for

illumination. The light scattered from the particles was observed by a CCD camera

or a photomultiplier tube (PMT). The PMT was used to measure the fluctuations in

scattered light caused by the particle moving in the trap. This enabled measurement

of the trap secular frequency.

Figure 5.8: The experimental setup of the PCB trap. The trap was housed in a vacuumchamber, and a piezo-speaker used to launch the particles flowing through theskimmer toward the trapping region. The trapped particle was then illumi-nated by an optical fibre which was embedded within the PCB and coupled toa 532 nm laser using a collimator and two mirrors. For imaging, a CCD cam-era is connected to a zoom lens to observe the scattered light from the trappedparticle. The CCD camera could be replaced by a PMT to measure the trapsecular frequency. The inset is a photograph of the PCB trap inside the vacuumchamber.

70

5.4.1.2 Trap evaluation

We initially investigated the ability to trap different masses in air and under vacuum.

The first attempt used 10 µm diameter silica particles, but these were difficult to

load into the trap in air, so it was decided to use near vacuum conditions. After

several attempts under vacuum, we obtained successful trapping at 1.6×10−1 mbar.

All relevant operating parameters for this trap are listed in table 5.1. A photograph

of the trapped particle is also shown in Fig 5.9. Assuming that we were trapping 10

µm diameter silica, the charge is limited by the stability parameters and expected to

be between 1×1.6×10−19 C ≤ Q ≤ 24070×1.6×10−19 C to satisfy the stability

condition (qu < 0.908). For Q = 1× 1.6× 10−19 C the Mathieu parameters are

ar = 3.5×10−7 and qr = 3.7×10−5.

Table 5.1: Operating parameters for trapping 10 µm silica under vacuum in a PCB trap.

Parameter ValueParticle size (diameter) 10 µm silica

Pressure 1.6×10−1 mbarVpeak−peak 810 Volt

U +20 VoltΩ 300 Hz

Figure 5.9: A photograph of 10 µm silica trapped under vacuum in the PCB trap. Thecharge is between 1×1.6×10−19 C≤Q≤ 24070×1.6×10−19 C based on theoperating parameters listed in table 5.1.

71

5.4.1.3 Limitation

The diverging light from the fibre tip dominated the scattered light from the trapped

particle. This made it difficult to measure the trap frequency. It was therefore

decided that a collimated beam should be used to illuminate the particle through

the top of the vacuum chamber. However, a major limitation of this trap was that

electrical breakdown occurred between the electrodes across the PCB substrate,

even after modifying the trap by adding an extra slot between AC and DC electrodes

as shown in Fig 5.10.

Figure 5.10: An extra slot was milled between the AC and DC electrodes in PCB trap.

It was decided to discontinue with this trap and, instead, continue with the linear

quadrupole with endcaps design, so that we could reliably trap particles without

breakdown. Although not used here, the PCB trap is currently being used for work

that relates to the cooling of silica nanoparticles in a hybrid system containing a

Paul trap and an optical trap [75].

5.4.2 Linear quadrupole trap with endcaps

5.4.2.1 Experimental set-up

The set-up for this trap is shown in Fig 5.12. The particles are loaded using three

different approaches. At the first stage, we used the piezo-speaker as we did for

the PCB trap, except that the piezo-speaker had a housing to guide particles toward

the trap centre as shown in Fig 5.11. At a later stage, an electrospray was used to

load the trap under vacuum and a nebuliser for loading at atmospheric pressure. For

illumination and detection, a similar set-up to that used in the PCB trap was used,

72

except that the optical fibre was attached to an adjustable collimator to focus the

laser beam used to illuminate the trapped particle.

Figure 5.11: A 3D model of part of the piezo housing.

Figure 5.12: The experimental setup of the linear quadrupole trap with endcaps. The trapwas housed in a vacuum chamber, and loaded using a piezo-speaker or anelectrospray. The piezo-speaker was placed underneath the trap (located in-side the vacuum chamber), and used to load the trap at atmospheric pressureor in near vacuum conditions, but not at high vacuum. An electrospray placedabove the trap was used for high vacuum loading. The trapped particle wasilluminated by a 532nm laser coupled to an optical fibre with an adjustablefocus collimator. The scattered light from the trapped particle was detectedby a CCD camera or a PMT.

73

5.4.2.2 Trap evaluation

Following the same process as with the PCB trap, we first tested the linear

quadrupole trap with endcaps at atmospheric pressure with two different sizes of

particle (10 µm and 2.5 µm) using the piezo-speaker. The only difference was that

the smaller particles were loaded using an ultrasonic nebuliser. The trap showed the

ability to levitate both sizes easily without an electrical breakdown between the trap

electrodes. The operating parameters are given in table 5.2. Based on these oper-

ating values, at atmospheric pressure, the charge for the 10 µm silica was between

1×1.6×10−19 C≤ Q≤ 63171×1.6×10−19 C, and for the 2.5 µm silica between

1×1.6×10−19 C≤ Q≤ 1542×1.6×10−19 C.

Under vacuum, the charge for the 10 µm silica was expected to be between

1× 1.6× 10−19 C ≤ Q ≤ 87504× 1.6× 10−19 C. An image of the trapped par-

ticle is shown in Fig 5.13. Note that the operating parameters for the 10 µm silica

varies between atmospheric pressure and under vacuum. This is due to the dif-

ference in the charge-to-mass ratio of the trapped particles, which are within the

stability region of the trap.

Figure 5.13: A photograph of a 10 µm silica particle trapped at 1.8×10−2 mbar in the lin-ear quadrupole trap with endcaps. The charge is between 1×1.6×10−19 C≤Q ≤ 87504 × 1.6 × 10−19 C based on the operating parameters given intable 5.2.

74

Table 5.2: Operating parameters for trapping 10 µm and 2.5 µm silica particles in the linearquadrupole trap.

Parameter ValueSilica diameter (µm) 10 10 2.5

Pressure (mbar) 1000 1.8×10−2 1000Vpeak−peak(Volt) 2000 282 2000

U (Volt) +31 +31 +31Ω (Hz) 400 250 500

The purpose of using silica particles was to understand how well the trap operated,

and to test our systems, before moving to smaller nanometer scale diamond beads.

After several attempts a 100 nm diamond was successfully trapped for the first

time. The settings are given in table 5.3, and a photograph of the trapped particle

is shown in Fig 5.14. The nanodiamonds were sourced from Adamas Nanotech-

nologies. Particle charge in the range of 1×1.6×10−19 C≤Q≤ 2×1.6×10−19 C

was expected, based on the stability parameter. It should be noted that we did not

consider the effect of air damping under vacuum in the stability region, where the

value of q is higher by a factor of up to 25 compared to no air damping [66]. We

can see here that the charge is limited to about two elementary charges based on

the operating values used. This is due to the low driving frequency and volt-

age, which are limited by the maximum output of the high voltage amplifier

(Vmax=2 kVpeak−peak) used in the experiment (Trek 2220). To trap highly charged

particles with smaller masses, we need a higher driving frequency with high AC

voltage as expected from the stability criteria.

Table 5.3: Operating parameters for trapping 100 nm diamond at atmospheric pressure inthe linear quadrupole trap.

Parameter ValueParticle size (diameter) 100 nm diamond

Pressure Atmospheric pressureVpeak−peak 2 kV

U +40 VoltΩ 2 KHz

75

Figure 5.14: A photograph of a 100 nm diamond trapped at atmospheric pressure in thelinear quadrupole trap with endcaps. The operating parameters are shown intable 5.3. The expected charge is between one or two elementary charges.

The next step was to trap 100 nm diamonds under vacuum to measure the secular

frequency. The piezo-speaker was replaced by an electrospray as discussed in sec-

tion 5.3 . We succeeded in trapping 100 nm diamond at 4× 10−3 mbar using the

trapping parameters given in table 5.4. It was now possible to measure the trap fre-

quency of the trapped particle by using the PMT. This was used to measure the fluc-

tuations in scattered light caused by the particle’s motion in the trap. The output cur-

rent of the PMT was connected to an oscilloscope, where it was converted to a time

varying voltage signal, and then recorded. By Fourier transforming the PMT signal,

it was possible to determine the trap frequencies as shown in Fig 5.15. We can see

that the driving frequency appears as the largest peak at 6.87 kHz with two side-

band peaks for ωz and ωx,y secular frequencies shifted by about 60 Hz and 209 Hz

respectively. A third peak, at 153 Hz, is related to the difference between the two

secular frequencies. We can estimate the particle radius R from the linewidth γg of

the secular frequencies peaks. This is given by [88, 89]:

γg =Γ0

2π=

12π

mGPrν

ρRkBT

(1+

π

8

). (5.5)

Here, Γ0 is the viscous damping factor caused by air, mG is the mass of the gas

molecule in amu unit, Pr is the pressure inside the chamber in Pascal, ρ and R are

the density and radius of the particle respectively, kB is the Boltzmann constant and

76

T is the temperature of the gas. The mean thermal velocity of the gas is given by

ν =√

8kBTπmG

. To define the linewidth γg of the secular frequencies peaks, we can fit

the power spectrum density (PSD) in Fig 5.15, where the time trace is in V2/Hz,

using the equation [90–92]:

S(ω) =2kBT

mγ2Γ0(

ω20 −ω2

)2+Γ2

0ω2, (5.6)

where m is the particle mass, γ is a calibration factor in V/m, ω0 is the secular

frequency and ω is the observed frequency. We used the following equation for

fitting:

S(ω) =A

(B2−ω2)2+C2ω2

+D, (5.7)

where A = 2kBT γ2Γ0m , B = ω0 and C = Γ0 are the fitting parameters and D is the

spectrum noise floor. The linewidth γg is about 3.21± 0.14 Hz. It is now possible

to calculate the radius of the trapped particle by using equation 5.5. This is about

R = 45±15 nm, this deviation in particle radius is due to uncertainty in the pressure

around the particle. We assumed that the pressure varied by a factor of two in the

range where the pressure transducer was located.

Table 5.4: Operating parameters for trapping 100 nm diamond at 4× 10−3 mbar in thelinear quadrupole trap.

Parameter ValueParticle size (diameter) 100 nm diamond

Pressure 4×10−3 mbarVpeak−peak 2000 Volt

U +31 VoltΩ 6.87 KHz

Electrospray 4050 Volt

77

6 . 6 6 . 7 6 . 8 6 . 9 7 . 0 7 . 1 7 . 21 0 - 1 0

1 0 - 9

1 0 - 8

1 0 - 7

1 0 - 6

1 0 - 5

γ g =2 . 6 2 H z

γ g =3 . 1 8 H z

γ g =3 . 2 7 H z γ g =3 . 3 1 H z

γ g =3 . 2 4 H z

γ g =3 . 6 9 H z

Ww x , y = 2 0 9 H zw z = 6 0 H z

W - ( w x , y - w z )

W - w x , y W - w z

W + ( w x , y - w z )

Powe

r spe

ctral

dens

ity (V

2 /Hz)

F r e q u e n c y ( k H z )

W = 6 . 8 7 k H z

W + w zW + w x , y

Figure 5.15: The measured trap frequency after trapping 100 nm diamond under4× 10−3 mbar in the linear quadrupole trap. The red line shows the exper-imental PSD, and the blue line represents the fitted PSD using equation 5.7.The AC frequency appears as the largest peak at 6.87 kHz, with two side-band peaks for ωz and ωx,y secular frequencies, shifted by about 60 Hz and209 Hz respectively. The peak at 153 Hz represents the difference betweenthe ωx,y and ωz secular frequencies. The average linewidth γg of the secularfrequencies peaks is 3.21±0.14 Hz, where the spectrum noise floor is about3.56×10−10 V2/Hz.

We can estimate the charge, Q, of the trapped particle by using equations 3.27. The

charge in this case was Q = 2× 1.6× 10−19 C. Sine we have now calculated the

charge and mass of the trapped particle, we can calculate the Mathieu parameters,

which are ar = 1.4×10−4, qr = 8.76×10−2, az = 2.8×10−4 and qz = 4.9×10−3.

It should be noted that the maximum charge allowed, based on the operating param-

eters, is about Q = 30×1.6×10−19 C.

To validate the experimental results, we simulated the particle motion inside the

trap by using the equations of motion described in the chapter 3, after considering

geometrical efficiency factors. The secular frequencies were then calculated by us-

ing the power spectrum of the simulated particle trajectory. The power spectrum in

Fig 5.16 resembles that of the experiment, with ωx,y and ωz secular frequencies of

60 Hz and 209 Hz respectively.

78

0 50 100 150 200 2500.000

0.005

0.010

0.015

0.020

0.025

Frequency (Hz)

Amplitude

(a.u.)

Figure 5.16: Simulated secular frequency in the linear quadrupole trap. The first peakat 60 Hz is the ωz secular frequency. The second peak, at 209 Hz, is ωx,y.The parameters used for the simulation are Ω = 6.87 KHz, Vpeak−peak = 2 kV,U = +31 V, Q = 2×1.6×10−19 C and R = 45 nm.

5.5 ConclusionIn this chapter, we described the construction and characterisation of the linear

quadrupole trap and the PCB trap. We explored how these traps can be loaded

with particles using three different approaches: including a piezo-speaker, a nebu-

liser and an electrospray. We found that each techniques was suitable for loading

but an electrospray needs to be used for vacuum, due to electrical breakdown.

As the PCB trap was found to discharge between the electrodes across the PCB

substrate, this trap will not be considered further for the proposed experiments.

The linear quadrupole trap, however, was capable of trapping various particle sizes

at atmospheric pressure, and under vacuum, without an electrical discharge. It

was therefore selected as the preferred design for trapping NV diamond. We also

demonstrated the trapping of 100 nm NV diamond in vacuum, which is the first

step toward the proposed matter-wave experiment. In the next chapter we will de-

scribe how a microwave antenna was integrated into this trap, and investigate NV

photoluminesence for an NV diamond within this trap.

Chapter 6

Microwave excitation of NV diamond

6.1 OverviewAn important requirement for spin manipulation in nanodiamonds, and eventually

for matter-wave interferometry, is a strong microwave field within the vicinity of the

NV centre. For nanodiamonds on surfaces, this is usually accomplished by using a

small wire to act as a near field antenna in very close proximity (less than 100 mi-

crons) to the nanodiamond. Such proximity is problematic in a Paul trap, where the

distance between the trapped particle and the electrode structure is usually greater

than a millimetre. In addition, the other electrode of the Paul trap can interfere with

the propagating microwave fields within the trap.

In this chapter, we study the fields created inside the Paul trap using different an-

tenna structures. We begin by reviewing microwave antennas that have previously

been used for NV excitation. We then explore the use of a microwave antenna that

is part of the electrode structure of a linear Paul trap. The effect of the other Paul

trap electrodes on the distribution of magnetic field strength and power density is

then calculated.

6.2 Different design geometriesWhile several antenna geometries are available, our focus is on those which have

been used for NV excitation of a levitated diamond. A microwave antenna with

a loop shape has been implemented in optically levitated diamond experiments

[93, 94]. For example, Horowitz et al and Hoang et al. [93, 94] used a loop antenna

80

printed on a glass coverslip with an outer diameter of about 2 mm. In this study by

Hoang et al.,the antenna was placed 0.5 mm from the levitated nanodiamod, while

a study by Neukirch et al. [29] used a simple wire with a thickness of 25 µm. This,

according to the authers, was as close as possible to the levitated nanodiamond.

For NV diamonds levitated in ion traps, Delord et al. [42] used a wire antenna placed

150 µm from the levitated microdiamond in a needle trap. The wire’s position could

be adjusted to optimise the microwave power on the NV’s in the microdiamond. In

a further experiment, Delord et al. replaced the needle trap with a loop electrode

trap, where the loop was also the microwave antenna [31]. This trap had an outer

diameter of 2 mm and an inner diameter of 1.4 mm [31].

In order to understand the utility of these antenna, we simulated the magnetic field

strength ~H (A/m) and the electric fields ~E (V/m) around the antennas. The power

density was calculated using the Poynting vector, ~S = ~E × ~H. The magnetic field

strength and the power density were modelled using CST (Computer Simulation

Technology) MICROWAVE STUDIO. This software discretizes Maxwells integral

equation for a particular electrode geometry using the finite integration technique

(FIT) [95].

To determine the approximate MW magnetic field strength required for excitation

of the NV spin, we first need to know what Rabi frequency is required to drive the

spin. The Rabi frequency f , driven by a magnetic field, B0, takes the form [96]:

f =12

geµBB0/h, (6.1)

where µB is the Bohr magneton, ge is the free-electron g-factor and h is the Planck

constant. The minimum magnetic field that can be used is determined by setting

the Rabi frequency to 1/T2, where T2 is the spin decoherence time. T2 is of order

of microseconds for bulk diamond and hundreds of nanoseconds for nanodiamond.

The minimum magnetic field strength H0, can be then calculated using:

H0 = B0/µrµ0, (6.2)

81

where µr is the relative permeability of the material and µ0 is the vacuum per-

meability. We can now calculate the minimum magnetic field strength H0 to be

approximately 0.6 A/m for bulk diamond (assuming T2 = 100 µs) and 57 A/m for

nanodiamond (assuming T2 = 1 µs). Initially, a loop antenna of a similar design to

that used by Delord et al. [31] was modelled, as shown in Fig 6.1. This is also a

similar geometry to that used in the optical traps discussed above.

Figure 6.1: 3D geometry of the loop antenna. The outer radius is 1 mm and the inner radiusis 0.7 mm. This geometry is obtained from reference [31].

The absolute value of the magnetic field strength |~H|, and the power density for this

antenna, were calculated, and are shown in Fig 6.2. The input power was 0.5 W.

(a) Side view of H-field contours. (b) Top view of H-field contours.

Figure 6.2: Plots of the absolute value of the magnetic field strength contours created by aloop antenna with 0.5 W of input power. The colour signifies the absolute valueof the magnetic field strength in A/m. The antenna has an inner radius 0.7 mmand a thickness of 0.3 mm.

82

- 4 - 3 - 2 - 1 0 1 2 3 4- 2 00

2 04 06 08 0

1 0 01 2 01 4 01 6 0

H S

x ( m m )

H (A/m

)

z

x y

01 x 1 0 5

2 x 1 0 53 x 1 0 5

4 x 1 0 5

5 x 1 0 5

6 x 1 0 5

S (W

/m2 )

T r a p c e n t r e

(a) |~H| and ~S along x axis.

- 2 . 0 - 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 5 2 . 005 0

1 0 01 5 02 0 02 5 03 0 03 5 04 0 0 T r a p c e n t r e

H S

y ( m m )

H (A/m

)

2 . 0 x 1 0 5

7 . 0 x 1 0 5

1 . 2 x 1 0 6

1 . 7 x 1 0 6

2 . 2 x 1 0 6

2 . 7 x 1 0 6

3 . 2 x 1 0 6

y

S (W

/m2 )

Left p

art of

the lo

op an

tenna

Right

part

of the

loop

anten

na

z

x y

(b) |~H| and ~S along y axis.

Figure 6.3: Calculated absolute value of the magnetic field strength for the loop antennawith an outer diameter of 2 mm and an inner diameter of 1.4 mm. The inputpower is 0.5 W. The power density is about 559 kW/m2 at the trap centre and221 kW/m2 at a distance of 0.5 mm from the centre.

The power density in the middle of the loop is 559 kW/m2 (143 A/m) and

221 kW/m2 (88 A/m), at a distance of 0.5 mm away from the centre as seen in

Fig 6.3. This is the distance to the optically trapped particle reported by Hoang et

al. [94]. The magnetic field strength generated is 2.5 times greater than the mini-

mum strength required for nanodiamond excitation at the loop centre. It is 1.5 times

greater at a distance of 0.5 mm from the centre.

83

6.3 Microwave antenna integrated into the Paul trapFor simplicity, we studied the integration of an antenna within a linear Paul trap

and calculated the microwave field within the cylindrical electrodes of the Paul trap

described in section 4.2. This trap consists of four parallel cylindrical electrodes.

For trapping, an AC voltage is applied to the two opposing electrodes, and the other

two are grounded.

One of the grounded electrodes is now used as a microwave antenna (+ x axis). The

isolation of the grounded electrode from the high frequency microwave signal is

accomplished by use of an inductor. This antenna can be approximately described

as a monopole antenna, in terms of its geometry and the radiation pattern gener-

ated. The monopole antenna consists of a metal rod, mounted perpendicular to a

grounded surface. A MW source is connected between the lower end of the rod and

this surface. The oscillating current generates a microwave field with a resonant

frequency that depends on the length of the antenna, L. If this length is equal to a

quarter wavelength of the radiation L = λ/4 (for an infinite ground plane), then the

power radiated from the antenna is at a maximum. This is because the antenna is

impedance matched with the MW source.

Because, in our case, the antenna had no ground plane, and its length (which could

not be changed because of trapping requirements) was 28% of the ideal value. That

means we expect a power loss due to an impedance mismatch between the antenna

input and the source output. This meant that the antenna could not be used for effi-

cient far field propagation. However, as we are only interested in near field coupling,

the power transmission (coupling) between the antenna and the NV diamond might

be sufficient for NV excitation. We decided to evaluate this possibility. The com-

puted magnetic field strength for the electrodes, where the input microwave power

is 16 W, is shown in Fig 6.4. The absolute value of the magnetic field strength,

and the power density along the x,y and z directions, are shown in Fig 6.5,a,b and c

respectively, where the origin is the centre of the trap.

84

(a) Side view of H-field contours.

(b) Top view of H-field contours.

Figure 6.4: The absolute value of magnetic field strength contours of the monopole an-tenna at an input power of 16 W. The colour signifies the absolute value of themagnetic field strength in A/m. The antenna length is 7 mm and its diameteris 4 mm.

At the trap centre, the magnetic field strength is about 4 A/m and the power density

is about 18.4 kW/m2. This power density is lower than for the loop antenna (which

was 559 kW/m2, as seen in the previous section).

The centre of the trap in this configuration is 1.75 mm away from the MW electrode

surface (at the same distance using the loop antenna with 0.5 W input power is

H = 11 A/m and S = 3.6 kW/m2). We can also see that the absolute value of

the magnetic field strength decreases along the z axis, since the antenna feedline

is attached to the upper end of the electrode at +3.5 mm (the electrode length is

7 mm). In order to produce the same magnetic field strength for this structure as the

loop antenna, we would need to use an input power of 556 W.

85

- 6 - 4 - 2 0 2 4 6 8 1 0 1 2 1 4012345678

zy H

S

x ( m m )

H (A/m

)

MW an

tenna

T r a p c e n t r e

x

01 x 1 0 42 x 1 0 43 x 1 0 44 x 1 0 45 x 1 0 46 x 1 0 47 x 1 0 48 x 1 0 4

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 54 . 04 . 5

H S

y ( m m )

H (A/m

)

E l e c t r o d e d i a m e t e r

zy

x

0 . 02 . 0 x 1 0 34 . 0 x 1 0 36 . 0 x 1 0 38 . 0 x 1 0 31 . 0 x 1 0 41 . 2 x 1 0 41 . 4 x 1 0 41 . 6 x 1 0 41 . 8 x 1 0 42 . 0 x 1 0 42 . 2 x 1 0 4

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 001234567

H S

z ( m m )

H (A/m

)

01 x 1 0 4

2 x 1 0 4

3 x 1 0 4

4 x 1 0 4

5 x 1 0 4

6 x 1 0 4

S (W

/m2 )

E l e c t r o d e l e n g t h

zy

x

(c) |~H| and ~S along z axis.

Figure 6.5: The absolute value of magnetic field strength and power density of a monopoleantenna at 16 W input power along x,y and z axes. At the trap centre, theabsolute value of the magnetic field strength is about 4 A/m, and the powerdensity is about 18.4 kW/m2.

86

Two further simulations were carried out in order to determine the effect of the

other trapping electrodes, as these will scatter radiation. Firstly, we performed a

calculation using the monopole antenna and the grounded electrode, with a sepa-

ration of 3.5 mm along the x axis. Fig 6.6 shows the variation in absolute value

of the magnetic field strength contours. We can see that, for this simple case, the

magnetic field strength is increased. From Fig 6.7, we can see that the magnetic

field strength is 4.73 A/m, and the power density is 23.92 kW/m2 at the trap centre.

This is an increase of about 30.4 % in the power density, compared to the monopole

microwave antenna/electrode alone. This is a result of constructive interference at

the trap centre.



Figure 6.6: Absolute value of the magnetic field strength contours of a monopole antennaat 16 W input power, after placing a second grounded electrode at a distance of3.5 mm.

87

- 1 5 - 1 0 - 5 0 5 1 0 1 50123456789

H S

x ( m m )

H (A/m

)

MW an

tenna

T r a p c e n t r e

Electr

ode

zy

x

0 . 0 01 . 5 0 x 1 0 4

3 . 0 0 x 1 0 4

4 . 5 0 x 1 0 4

6 . 0 0 x 1 0 4

7 . 5 0 x 1 0 4

9 . 0 0 x 1 0 4

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00

1

2

3

4

5 H S

y ( m m )

H (A/m

)

E l e c t r o d e d i a m e t e r

zy

x

0 . 05 . 0 x 1 0 3

1 . 0 x 1 0 4

1 . 5 x 1 0 4

2 . 0 x 1 0 4

2 . 5 x 1 0 4

3 . 0 x 1 0 4

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00123456 H

S

z ( m m )

H (A/m

)


zy

x

01 x 1 0 42 x 1 0 43 x 1 0 44 x 1 0 45 x 1 0 46 x 1 0 47 x 1 0 48 x 1 0 4

S (W

/m2 )


Figure 6.7: Calculated absolute value of magnetic field strength and power density of amonopole antenna, after placing the second grounded electrode on x,y and zaxes. At the trap centre, the magnetic field strength is around 4.73 A/m withpower density around 23.91 kW/m2.

88

Next, we calculated the effect of all the trap electrodes. In this case, we con-

sidered the electrodes as ungrounded metal. The absolute value of the magnetic

field strength that is shown in Fig 6.8. Interestingly, the power density dropped to

about 13.7 kW/m2 and the magnetic field strength was around 3.4 A/m as shown in

Fig 6.9. This drop is about 25.5 % of the power density calculated for the single

monopole antenna. This configuration would require an input power of 654 W to

reach the absolute value of the magnetic field strength achieved in the experiments

of DeLord et al. [31].



Figure 6.8: Absolute value of magnetic field strength contours of a monopole antenna at16 W input power, when all quadrupole electrodes are taken into account.

89

- 1 5 - 1 0 - 5 0 5 1 0 1 50123456789 H

S

x ( m m )

H (A/m

)

T r a p c e n t r e

MW an

tenna

Electr

ode

zy

x

0 . 0 01 . 5 0 x 1 0 43 . 0 0 x 1 0 44 . 5 0 x 1 0 46 . 0 0 x 1 0 47 . 5 0 x 1 0 49 . 0 0 x 1 0 41 . 0 5 x 1 0 5

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00 . 00 . 51 . 01 . 52 . 02 . 53 . 03 . 5

H S

y ( m m )

H (A/m

)

zy

x

0 . 02 . 0 x 1 0 34 . 0 x 1 0 36 . 0 x 1 0 38 . 0 x 1 0 31 . 0 x 1 0 41 . 2 x 1 0 41 . 4 x 1 0 4

S (W

/m2 )

Electr

ode

Electr

ode


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00123456

H S

z ( m m )

H (A/m

)

01 x 1 0 42 x 1 0 4

3 x 1 0 4

4 x 1 0 4

5 x 1 0 46 x 1 0 4

7 x 1 0 4

S (W

/m2 )


zy

x


Figure 6.9: Absolute value of magnetic field strength and power density of the monopoleantenna after placing all quadrupole electrodes along the x,y and z axes. Theabsolute value of the magnetic field strength is about 3.4 A/m with a powerdensity of 13.7 kW/m2 at the trap centre.

90

To understand this drop in power density, we simulated the use of only two parallel

AC electrodes in the y direction with the microwave antenna. First, we simulated

the use of only one the electrodes, and then both. This comparison is shown in

Fig 6.10.

- 1 . 5 - 1 . 0 - 0 . 5 0 . 0 0 . 5 1 . 0 1 . 52 . 5 x 1 0 3

7 . 5 x 1 0 3

1 . 3 x 1 0 4

1 . 8 x 1 0 4

2 . 3 x 1 0 4 E l e c t r o d e

T r a p c e n t r e

S (W/

m2 )

x ( m m )

M W a n t e e n a

Figure 6.10: A comparison of power density along x-axis for all the quadrupole configura-tions. At the trap centre, the power density for the microwave antenna aloneis about 18.4 kW/m2, 14.7 kW/m2 with one AC electrode, 11.4 kW/m2 withtwo AC electrodes, 24 kW/m2 with the grounded electrode and 13.7 kW/m2

with all electrodes.

The effect of placing the AC electrodes leads to a drop in the power and mag-

netic field strength because the two AC electrodes reflect the field and prevent it

from propagating into the centre of the gap between the electrodes. By placing one

AC electrode (the upper or the lower electrode) the power density drops by 20%

(H=3.52 A/m, S=14.7 kW/m2) and by placing both electrodes the drop is about

38% (H=3.03 A/m, S=11.4 kW/m2). In general, the AC electrodes decrease the

power density in the gap where the particle would be trapped. The grounded elec-

trode, in parallel with the same axis of the antenna electrode, increases the power

at the trap centre. Placing all electrodes will result in a drop of 25.5% in power

density, compared to a single electrode acting as the microwave antenna.

As noted in the previous section, more power could be obtained, in general, by us-

91

ing a loop antenna. The principal reason for this is that the feedline is connected to

one end of the antenna, and the other end is grounded. The monopole antenna, on

the other hand, has no grounded end. With this in mind, the idea of connecting the

two grounded electrodes in a loop, which would be closer a the loop antenna, seems

feasible. We examined this idea, using a linear Paul trap to form a loop antenna.

The absolute value of the magnetic field strength for this arrangement is shown in

Fig 6.11. Further, we can see in Fig 6.12 that the magnetic field strength increases

to 83 A/m with a power density of about 911 kW/m2 at the trap centre. This is an

increase of 480% in power density compared to the monopole antenna.



Figure 6.11: Absolute value of the magnetic field strength of a loop antenna formed fromtwo grounded electrodes of the quadrupole trap without AC electrodes. Inputpower was 16 W. The straight section of the loop is 7 mm in length with3.5 mm separation.

92

- 1 4 - 1 2 - 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 0 1 2 1 401 02 03 04 05 06 07 08 09 0

1 0 01 1 01 2 0

H S

x ( m m )

H (A/m

)

Left p

art of

the lo

op an

tenna

Right

part o

f the lo

op an

tenna

T r a p c e n t r e

z

y x

0 . 02 . 0 x 1 0 5

4 . 0 x 1 0 5

6 . 0 x 1 0 5

8 . 0 x 1 0 5

1 . 0 x 1 0 6

1 . 2 x 1 0 6

1 . 4 x 1 0 6

1 . 6 x 1 0 6

1 . 8 x 1 0 6

S (W

/m2 )


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 001 02 03 04 05 06 07 08 0 H

S

y ( m m )

H (A/m

)

1 . 0 0 E + 0 52 . 5 0 E + 0 54 . 0 0 E + 0 55 . 5 0 E + 0 57 . 0 0 E + 0 58 . 5 0 E + 0 51 . 0 0 E + 0 6

S (W

/m2 )

L o o p t h i c k n e s s

z

y x

(b) |~H| and ~S y axis.

- 1 2 - 1 0 - 8 - 6 - 4 - 2 0 2 4 602 04 06 08 0

1 0 01 2 01 4 01 6 01 8 02 0 0

H S

z ( m m )

H (A/m

)

S t r a i g h t p a r t o f t h e l o o p a n t e n n a

Upper

part

of the

loop

anten

na z

y x

0 . 02 . 0 x 1 0 64 . 0 x 1 0 66 . 0 x 1 0 68 . 0 x 1 0 61 . 0 x 1 0 71 . 2 x 1 0 71 . 4 x 1 0 7

S (W

/m2 )


Figure 6.12: Absolute value of magnetic field strength and power density of the loop an-tenna formed from two grounded electrodes of the quadrupole trap, withoutthe AC electrodes on x,y and z axes. The absolute value of the magnetic fieldstrength is about 83 A/m, and power density is about 911 kW/m2 at the trapcentre.

93

By placing the other two AC electrodes to form the complete trap, as shown in

Fig 6.13, we see a drop of 30.5% in power density, compared with the case with no

AC electrodes. The absolute value of the magnetic field strength at the trap centre

was 64 A/m, and the power density was 633 kW/m2 as shown in Fig 6.14. This

magnetic field strength is lower by a factor of 2, compared to the loop antenna used

by DeLord et al. [31], but is still high enough for NV nanodiamond excitation.

z

y

x

Feeding

port

Figure 6.13: Absolute value of the magnetic field strength of the loop antenna formed fromtwo grounded electrodes of the quadrupole trap, with 16 W input power. Thestraight part of the loop is 7 mm in length, and seperation is 3.5 mm.

94

- 1 4 - 1 2 - 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 0 1 2 1 401 02 03 04 05 06 07 08 09 0

1 0 01 1 0 H

S

x ( m m )

H (A/m

)

0 . 02 . 0 x 1 0 54 . 0 x 1 0 56 . 0 x 1 0 58 . 0 x 1 0 51 . 0 x 1 0 61 . 2 x 1 0 61 . 4 x 1 0 61 . 6 x 1 0 61 . 8 x 1 0 62 . 0 x 1 0 6

S (W

/m2 )

Right

part

of the

loop

anten

na

Left p

art of

the lo

op an

tenna

T r a p c e n t r e


- 1 0 - 8 - 6 - 4 - 2 0 2 4 6 8 1 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0 H S

y ( m m )

H (A/m

)

1 . 0 0 E + 0 5

2 . 5 0 E + 0 5

4 . 0 0 E + 0 5

5 . 5 0 E + 0 5

7 . 0 0 E + 0 5

S (W

/m2 )

Electr

ode

Electr

ode

L o o p t h i c k n e s s


- 1 2 - 1 0 - 8 - 6 - 4 - 2 0 2 4 602 04 06 08 0

1 0 01 2 01 4 01 6 01 8 02 0 02 2 0

H S

z ( m m )

H (A/m

)

S t r a i g h t p a r t o f t h e l o o p a n t e n n a

Upper

part o

f the lo

op an

tenna

0 . 02 . 0 x 1 0 6

4 . 0 x 1 0 6

6 . 0 x 1 0 6

8 . 0 x 1 0 6

1 . 0 x 1 0 7

1 . 2 x 1 0 7

1 . 4 x 1 0 7

1 . 6 x 1 0 7

S (W

/m2 )


Figure 6.14: Absolute value of magnetic field strength and power density of the loop an-tenna formed from two grounded electrodes of the quadrupole trap along thex, y and z axes. The absolute value of the magnetic field strength is about64 A/m with power density of 633 kW/m2 at the trap centre.

95

6.4 ConclusionWe studied a range of different microwave antenna designs which are integrated

into a Paul trap which will be used for NV excitation of levitated NV diamond.

The minimum magnetic field strength required for NV excitation is approximately

0.6 A/m for bulk diamond assuming T2 = 100 µs (common for bulk diamond), and

57 A/m for nanodiamond assuming T2 = 1 µs. Our calculations showed that the lin-

ear quadrupole design, which incorporates a single antenna, generates a magnetic

field strength of 3.4 A/m using 16 W input power, which is available for the experi-

ment. This will be suitable at least for NV microdiamond, and may be suitable for

very clean nanodiamond.

We also showed that a higher field strength can be obtained by connecting the two

ground electrodes which, by forming a loop antenna, would radiate more microwave

power (64 A/m). However, integrating this design into our trap would require re-

engineering the trap geometry to fit the DC endcaps, so this will not be considered

further at this stage. This decision could be reconsidered at a later stage, if the

power generated by the monopole antenna is not sufficient for NV excitation. We

will investigate this experimentally, as described in chapters 7 and 8.

Chapter 7

NV photoluminescence with

temperature, laser intensity and gas

pressure

7.1 OverviewThis chapter describes a study of the photoluminescence (PL) of micron-sized dia-

mond embedded with NV centres, and placed within the Paul trap but on a micro-

scope glass slide. This study was undertaken to understand and evaluate the NV

excitation and detection system before carrying out levitation experiments. We be-

gin with a description of the microwave source used in this experiment, then outline

the ODMR experiments performed with it. Measurements of the NV photolumi-

nescence (PL) as a function of pressure, temperature and laser intensity are also

presented.

7.2 Microwave sourceFor the ODMR experiments a, voltage-controlled oscillator VCO (ZX95-3050A+

from Mini-Circuits) was used to generate microwave (MW) signals from 2150 to

3050 MHz, with an output power of 5 mW. This signal was amplified to 16 W

by using a high power amplifier HPA (ZHL-16W-43+ from Mini-Circuits). One

of the ground electrodes in the linear quadrupole trap was used as a microwave

97

antenna without further fabrication or modification of the design. As shown in

Fig 7.1, the output signal from the HPA was fed into the upper-right ground elec-

trode of the linear quadrupole trap. This meant that the two ports (GND and MW)

were simultaneously connected to the upper right electrode. A toroidal inductor

(MCAP109020040K-101MU from multicomp) with a 100 µH inductance was con-

nected between the other end of the ground electrodes, allowing DC currants to pass

through the electrode while blocking the MW signal.

MW

AC

ACGND

GND

&

MW

High Voltage

AC

GND

Vacuum chamber

VCO HPA

Figure 7.1: A schematic diagram of the microwave source. The set-up consists of a volt-age controlled oscillator (VCO) to generate microwave (MW) signals. Thesewere amplified to 16 W using a high power amplifier (HPA). The output sig-nal from the HPA was then fed into the upper-right ground electrode of thelinear quadrupole trap. A toroidal inductor with 100 µH inductance was con-nected between the other ends of the ground electrodes. This allows DC currentthrough the lower left electrode but blocks the MW signal.

7.3 ODMR detection set-upWe have demonstrated a cost-effective system for ODMR detection. This system

consisted of a microwave source (VCO and HPA), power splitter PS (ZFRSC-42-S+

from Mini-Circuits), an avalanche photodiode APD (SPCM-AQRH-13 from Perkin

Elmer), a data acquisition DAQ (USB-6003 from national instruments) and a fre-

quency counter (TF960 from Thurlby Thandar Instruments). This was controlled

using a Labview program. A schematic of this system is shown in Fig 7.2.

98

HPAVCO PS

USB Remote control

TF930Frequency Counter

Frequency

Count

Labviewprogram

Optical fibrePaul Trap

DAQ

APD

Figure 7.2: A schematic diagram of the ODMR detection set-up. The system consistedof a microwave source (VCO and HPA), power splitter (PS) and avalanchephotodiode (APD). Also shown is the data acquisition card (DAQ), frequencycounter and Labview program used to acquire the data. The Labview programwas connected to the DAQ to tune the VCO voltage, and the output frequencyof the VCO was split into two signals using the PS. One signal was amplifiedby the HPA, then fed to the MW electrode of the trap; the other signal wasconnected to the frequency counter to measure the output frequency. The dropin fluorescence intensity, due to microwave excitation when in resonance withspin transition, was detected by the APD. The output TTL pulses from the APDwere counted by the frequency counter, which was recorded on the computerrunning Labview. The program plots the MW frequency as a function of photoncount during the experiment.

The Labview program controlled the DAQ, which was tuned the MW frequency. It

also readout the photon counts that came from the APD via the frequency counter.

The program also controlled the VCO input voltage through the DAQ. The in-

put voltage was scanned between 7 V and 9 V in 0.01 V steps, which tuned

the frequency between 2.765±0.1 GHz to 2.975±0.1 GHz with a resolution of

1.05 ± 0.05 MHz. The VCO frequency output was split into two signal compo-

nents. One component was directed to the HPA, and then fed to the MW elec-

trode of the trap; the other component of the signal was connected to the frequency

counter which was used to measure its frequency. To record the photon count from

the APD, the TTL output signal was connected to the frequency counter. It should

be noted that this setup had a minimum update time of 0.3 s for reading the photon

count and the frequency input (total of 0.6 s for both), which meant that the system

99

took approximately 2 minutes to scan 200 MHz in 1 MHz steps. This is sufficient

to record an NV spectrum.

7.4 Experimental set-upMicron sized diamond powder (from Columbus Nanoworks) with a high concentra-

tion of NV centres was used for all experiments in this chapter. This relatively high

concentration allowed us to obtain strong photoluminescence signals. A syringe tip

was used to place and position the particles on a microscope cover slide. A drop

of ethanol was then added, to enhance adhesion between the particles and the slide.

The glass slide was then placed vertically between the trap electrodes, as shown

in Fig 7.3. A photographic image of the deposited particles is shown in Fig 7.4,

where the size of the deposited particles is about (20± 8)µm. This is determined

by calibrating the image against the known separation between the two Paul trap

electrodes, visible as the darker regions in Fig 7.4.

Vacuum chamber

PumpVacuum

gauge

Optical fibre

Collimator Optical fibre to

APD or spectrometer

MW

Glass coverslip

NF LPFND

ALAL

CCD

camera

Figure 7.3: A schematic of the experiment. A microscopic glass slide was inserted ver-tically between the trap electrodes. The upper-right electrode was used formicrowave excitation. An optical fibre connected to a collimator was used fora 532 nm laser excitation. The optical detection set-up consisted of two 50 mmachromatic lenses (AL) to collect the fluorescence emission, a neutral densityfilter (ND) with optical density = 2, a notch filter centred at 532 nm (NF), alongpass filter (LP) with a cut-off wavelength of about 610 nm, and an opticalfibre attached to the APD or the spectrometer. A CCD camera was used forimaging of the particle.

100

Figure 7.4: Photograph of the deposited particles, the pixel density is 4 µm/pixel, and thediameter is (20± 8)µm. The sub-images are close-ups of the deposited parti-cles with the laser on and off.

7.5 Recorded NV spectraIt was essential to identify the NV spectrum using a spectrometer (Andor Shamrock

303i spectrograph, with 1200 lines/mm grating and 40 nm bandpass), to ensure the

optical alignment and to test the microwave system used for ODMR. The spectrom-

eter split the incident light into individual narrow bands of wavelength, and each

band interacted with an array of pixels across the EMCCD camera for a given expo-

sure time. The EMCCD signal was converted into a voltage, which was then readout

as a digitized unit called a “count” which is divided by the exposure time. Fig 7.5

shows the PL spectrum obtained using 32 mW of laser power, with an intensity of

10.2 kW/cm2, and a 1.5 s exposure time of the EMCCD camera. The spectrum

was acquired between 500 nm to 900 nm. The zero phonon line (ZPL) of the NV−

within the sample was observed at 640 nm (Fig 7.6) as described in section 2.1. A

microwave field was then switched on and tuned to 2.867 GHz to get the maximum

reduction in the PL count. This reduction was calculated by subtracting the count

from the total area of the spectrum before and after applying the microwave field

with no background subtraction. The reduction in the total count was about 11%.

The optical contrast was expected to be in the range of 30%, this is because the NV

101

has been shown to be ≤ 30% of the time in the dark NV0 state [33, 34].

6 0 0 6 4 0 6 8 0 7 2 0 7 6 0 8 0 0 8 4 0 8 8 02 5 0

1 2 5 0

2 2 5 0

3 2 5 0

4 2 5 0

5 2 5 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )

Z P L

Figure 7.5: Spectrum of NV centre using a power intensity of 10.2 kW/cm2 and 1.5 s expo-sure time. The red line represents the spectrum acquired without the microwavefield, and the blue line represents the spectrum with the microwave field tunedto 2.867 GHz. The total PL count decreased by 11% with the microwave fieldswitched on.

6 3 0 6 3 5 6 4 0 6 4 5 6 5 0

2 5 0

3 7 5

5 0 0

6 2 5

Photo

lumine

scen

ce (c

ounts

/s)


Figure 7.6: A close-up of NV− zero phonon line (ZPL). The laser intensity is 10.2 kW/cm2

and the exposure time is 1.5 s. The red line represents the spectrum acquiredwithout the microwave field, and the blue line represents the spectrum with themicrowave field. The PL intensity decreased by switching on the microwavefield at 2.867 GHz. This was due to excitation between the ms = 0 and ms =±1levels.

102

7.6 Optically detected magnetic resonanceAs described in sections 2.1 and 2.2, the ms = ±1 levels of NV diamond are off-

set from the ground state ms = 0 by 2.87 GHz and this is known as the Zero Field

Splitting (ZFS). To manipulate the spin state, we performed an electron spin reso-

nance (ESR) measurement by tuning a microwave field across the ESR resonance

to determine the ZFS. This resonance was observed as a reduction of PL count due

to the transition from the ms = 0 state to the ms = ±1 state and as a dip in the

recorded ESR spectrum. This process is called Optically Detected Magnetic Reso-

nance (ODMR). The ODMR detection set-up described earlier in this chapter was

used to perform this measurement. The ODMR spectrum was acquired between

2.77 GHz and 2.96 GHz with 1 MHz resolution at a laser intensity of 0.47 kW/cm2

as shown in Fig 7.7. The line shape of the ODMR spectrum could be described by a

Gaussian profile [23, 31], a Lorentzian profile [37, 97, 98] or a Voigt profile (a con-

volution of about 98% Lorentzian and 2% Gaussian) [99]. In our case, the shape is

a better fit to a Lorentzian rather than a Gaussian profile [97], especially for power

broadened ODMR as in our case [100]. It is worth mentioning that splitting of a

few MHz could be detected with no external magnetic field, due to the local crystal

strain field [37]. Therefore, when fitting the data, the ODMR dip was considered as

the midpoint of the two split dips. The ZFS was found to be 2.872±0.001 GHz as

expected for NV diamond at room temperature [32]. The ODMR contrast was about

17 ± 1 % which is expected since NV spends up to ≤ 30% of the time in the dark

NV0 state [33]. The peak width was about 70 MHz, which is considerably wider

than expected from the literature; typically around 5 MHz [37]. This broadening

could be related to the high RF power generated by the microwave source [97,101],

which is not adjustable in the current set-up.

103

2 . 8 0 2 . 8 5 2 . 9 0 2 . 9 50 . 7 5

0 . 8 0

0 . 8 5

0 . 9 0

0 . 9 5

1 . 0 0

Norm

alize

d PL c

ount

F r e q u e n c y ( G H z )

Figure 7.7: An ODMR spectrum at 0.47 kW/cm2. The red dots represent the measureddata while the red line represents a Lorentzian fit to the data. The shaded areais the error envelope for 2σ which is about ± 1 %. The plot is normalisedby the maximum output photon count, which represents the number of TTLoutput pulses from the APD within 1.5 s of exposure time. The ODMR dip wasconsidered as the midpoint of the two dips when fitting the data.

We also obtained spectra under three different laser intensities, but with the same

microwave field as seen in Fig 7.8. It can be seen that the ODMR contrast reduces

with higher laser intensity with a slight shift of the ZFS frequency below 2.87 GHz

as seen from the single Lorentzian fit in Fig 7.8. This data is summarised in table

7.1. The ZFS frequency shift and the reduction of the ODMR contrast is caused by

heat generated from the laser. This heat will increase the NV diamond temperature

and consequently increase the probability of non-radiative transition through the

singlet state.

Table 7.1: ZFS frequency and ODMR contrast obtained from ODMR spectra in Fig 7.8.

Laser Intensity (kW/cm2) ZFS Frequency (GHz) ODMR Contrast (%)0.47 2.8719 ± 0.0008 17 ± 1

3 2.8689 ± 0.0003 15 ± 0.510.2 2.8670 ± 0.0003 11 ± 0.4

104

2 . 8 0 2 . 8 5 2 . 9 0 2 . 9 50 . 7 50 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

0 . 7 50 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

0 . 4 7 k W / c m 2Norm

alize

d PL c

ount

0 . 7 50 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

Norm

alize

d PL c

ount

3 k W / c m 2

Norm

alize

d PL c

ount


1 0 . 2 k W / c m 2

Figure 7.8: The ODMR spectrum at laser excitation intensities of 0.47, 3 and 10.2 kW/cm2.Each line is a single Lorentzian fit of the data, and the shaded area is the errorenvelope for 2σ . A few MHz splitting was detected, with no magnetic field,due to internal strain. The ODMR dip was considered as the midpoint of thetwo dips when fitting the data. The ODMR contrast reduces as laser intensityincreases, and there is a slight shift in resonance frequency. This is probablydue to the heat generated in the crystals from absorption of the laser.

105

7.7 Zeeman splitting of ODMR spectraIn section 2.2, we discuss the effect of an external magnetic field (B) on the ODMR

spectra. In the presence of a magnetic field, the degeneracy of the ms = ±1 is lifted

by the Zeeman effect. The ODMR spectrum has two dips due to each ms = ±1

states. The separation in frequency (4ν) between these two dips changes with the

strength of the applied magnetic field B as:

4ν = 2γB, (7.1)

where γ = 28024.951 MHz/T is the electron gyromagnetic ratio.

The ODMR spectrum for different laser intensities, with an external magnetic field,

is shown in Fig 7.9. The magnetic field was generated by a neodymium magnet

placed inside the vacuum chamber. As in the field-free case above, a reduced

contrast occurs with increased laser intensity (7.6). The data showing the ESR fre-

quency shift in both peaks, resulting from increasing laser intensity, is summarised

in table 7.2.

Table 7.2: Frequency resonances and ODMR contrast obtained from split ODMR spectrain Fig 7.9.

Laser Intensity LeftFrequency Resonance

RightFrequency Resonance ODMR Contrast

(kW/cm2) (GHz) (GHz) (%)

0.47 2.84795 ± 0.0010 2.90493 ± 0.0012 12.4 ± 0.43 2.84803 ± 0.0006 2.89631 ± 0.0006 7.4 ± 0.2

10.2 2.84633 ± 0.0007 2.89086 ± 0.0008 5.2 ± 0.3

106

0 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

Norm

alize

d PL c

ount

0 . 4 7 k W / c m 2

0 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

Norm

alize

d PL c

ount

3 k W / c m 2

2 . 8 0 2 . 8 5 2 . 9 0 2 . 9 50 . 8 00 . 8 50 . 9 00 . 9 51 . 0 0

Norm

alize

d PL c

ount


1 0 . 2 k W / c m 2

Figure 7.9: Zeeman splitting of an ODMR spectrum at 0.47, 3 and 10.2 kW/cm2. The dotsrepresent the experimental data, the dashed lines represent the a Lorentzian fitof each peak, while the solid lines represent the sum of two Lorentzian peakscorrelated with the ms = +1 and ms = −1 states. The shaded area is the errorenvelope for 2σ . The ODMR spectrum experiences a Zeeman-shift due to anexternal magnetic field generated by a neodymium magnet. The two fluores-cence frequencies correlated with the ms = ±1 states appeared as two dips inthe spectrum. As with a typical ODMR spectrum, the heat generated from thelaser reduces the ODMR contrast with a slight shift in the resonance frequency.

107

A comparison of the ODMR spectrum with and without an external magnetic field

is shown in Fig 7.10. The separation in frequency between the two spin states is

48 MHz, which is consistent with that produced by a magnetic field of 0.84 mT

using equation 7.1. The magnetic field strength was measured using a commercial

Gaussmeter (Hirst Magnetics GM07), with the probe placed between the trap elec-

trodes, in the same position as with the diamond sample. The measured magnetic

field strength was 0.82±0.04 mT, which was consistent with the calculated value.

All measurements were carried out at this fixed magnetic field strength. We have

assumed that most of the NVs within the sample have the same orientation, and that

their axes are parallel to the magnetic field. If this were not the case, we should

observe more than two dips in the ODMR spectrum. This conclusion is consistent

with the observation reported by Fukui et al. [39]. It is probable, however, that other

orientations exist at lower density, and we cannot resolve them.

2 . 8 0 2 . 8 5 2 . 9 0 2 . 9 50 . 8 5

0 . 8 8

0 . 9 1

0 . 9 4

0 . 9 7

1 . 0 0

B = 0 TB » 0 . 8 4 m T

Norm

alize

d PL c

ount


Figure 7.10: Comparison between the ODMR signal with and without external magneticfield at 3 kW/cm2. The two resonance dips are separated by 48.3 MHz, whichis the same as the seperation in a magnetic field strength of 0.84 mT. Thecontrast dropped from 15 ± 0.5% with no magnetic field, to 7.4 ± 0.2% witha magnetic field.

108

7.8 Photoluminescence as a function of pressureThe PL at different laser intensities and pressures was studied. The average PL level

as a function of laser intensity (also called a PL saturation curve) is illustrated in

Fig 7.11. These measurements were taken with an APD and each data point is an

average of 10 measurements with a 1.5 s exposure time per measurement.

1 3 5 7 9 1 1 1 3 1 5 1 7 1 9

1 . 0

3 . 0

5 . 0

7 . 0

9 . 01 ´ 1 0 + 3 m b a r4 . 5 ´ 1 0 - 1 m b a r2 . 2 ´ 1 0 - 4 m b a rF i t u s i n g I P L ( L ) = I ( L / L + L s a t ) U n e x p e c t e d P L i n c r e a s e d u e t o

i m p u r i t i e s i n t h e s a m p l e P o l y n o m i a l f i t L i n e a r f i t

PL in

tensit

y (´1

06 coun

ts/s)

L a s e r i n t e n s i t y ( k W / c m 2 )Figure 7.11: PL saturation curves at different pressures. Lowering the pressure reduces the

PL count rate until it saturates. At this point, it starts quenching due to theincreased temperature of the diamond lattice. As the background gas acts asa heatsink, lower pressure causes an increase in internal temperature, whichincreases the probability of the non-radiative transition through the singletstate. The data at atmospheric pressure was fitted using equation 7.2, whereI∞ = 27 Mcounts/s and Lsat = 31 kW/cm2. This equation shows good agree-ment with the experimental data at atmospheric pressure, though not when thePL intensity starts to decline under vacuum. The data was fitted using a thirdorder polynomial, which was found to be in very good agreement with thethree different pressure levels. The unexpected increase due to impurities inthe sample was not included in the fitted data.

At atmospheric pressure, the fluorescence intensity increases linearly as a func-

tion of laser intensity. It then starts to saturate when the intensity is higher than

6.5 kW/cm2, due to an increased probability of non-radiative transitions through

the singlet state. This behaviour at atmospheric pressure has been previously ob-

109

served and the relationship between PL intensity IPL and laser intensity is given

by [102] :

IPL(L) = I∞(L

L+Lsat), (7.2)

where I∞ is the maximum intensity of the PL emission for infinitely high laser in-

tensity and Lsat is the laser intensity related to I∞.

It was found that, under vacuum conditions, this effect was enhanced. By reducing

the pressure to 4.5× 10−1 mbar, from atmospheric pressure (1000 mbar), the PL

intensity reaches a maximum at 11.5 kW/cm2, but then decreases at higher laser

intensities. This suppression of PL at higher intensities has been observed before,

and is believed to be due to the increase in temperature of NV diamond up to about

300 - 400 C (573.15 K - 673.15 K) [103, 104]. To verify that this reduction in

intensity is due to the NV, and not the excitation of impurities in the diamond or

optical components, we acquired spectra with a spectrometer, and measured how

the spectrum changed with laser intensity. This was carried out with two dif-

ferent laser intensities, each at two different pressures (atmospheric pressure and

4.5×10−1 mbar). These results are shown in Fig 7.12. The resulting spectra showed

similar behaviour to the PL saturation curves (Fig 7.11) at the same pressures.

The NV centre has two charge states NV− and NV0, and both can be transformed to

the other state [105, 106]. It is possible that laser excitation can prduce this change

in state. If so, we should observe a shift of the NV− spectrum (PL spectrum centred

at 680 nm) due to the increased presence of NV0 (PL spectrum centred at 610 nm)

states, so that the whole PL spectrum is centred between 610 nm and 680 nm in-

stead of 680 nm. However, by normalizing, and comparing two PL spectra at both

intensities (one at maximum intensity and the other at reduced intensity), we can see

(Fig 7.13) that there was, in fact, no shift in the spectrum. This is in agreement with

the findings of Plakhotnik and Chapman [103] who did not observe any transforma-

tion of the charge state with high laser intensity.

110

6 0 0 6 4 0 6 8 0 7 2 0 7 6 0 8 0 0 8 4 0 8 8 05 0 0

1 5 0 0

2 5 0 0

3 5 0 0

4 5 0 0

5 5 0 0

6 5 0 0

Photo

lumine

scen

ce (c

ounts

/s)


A t m o s p h e r i c a t 1 0 k W / c m 2

A t m o s p h e r i c a t 1 5 k W / c m 2

4 . 5 ´ 1 0 - 1 m b a r a t 1 0 k W / c m 2

4 . 5 ´ 1 0 - 1 m b a r a t 1 5 k W / c m 2

Figure 7.12: A PL spectrum at atmospheric pressure and at 4.5× 10−1 mbar. The spectrawere acquired for two laser intensities: 10 kW/cm2 and 15 kW/cm2, chosen torepresent the spectrum at the PL saturation level, and where the PL intensitywas quenched at 4.5×10−1 mbar. The intensities of these spectra demonstratethat the saturation and quenching of the fluorescence was connected to the NVdiamond.

6 0 0 7 0 0 8 0 0 9 0 00 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

Relat

ive PL

sign

al


Figure 7.13: A comparison of two PL spectrum profiles at 4.5× 10−1 mbar. The red linerepresents the spectrum at 10 kW/cm2 while the blue line represents the spec-trum at 15 kW/cm2. Each spectrum is normalized, so that the spectrum peakhas a high point of 1. The first spectrum is at 10 kW/cm2, which is the satu-ration level, and the other is at 15 kW/cm2 where the intensity declined. Noshifts of spectra was observed, because there is no change in the charge statefrom negative NV− to neutral NV0.

111

A further investigation was carried out at the higher vacuum level of at

2.2× 10−4 mbar. In this case, the saturation level was reached at 10 kW/cm2

followed by a reduction in the PL. However, at higher laser intensity, the fluores-

cence count increased, a result which has not been previously observed. A wide

scan of the PL spectrum indicates that this rise in the PL is not associated with

the characteristic NV spectrum (Fig 7.14), but is probably due to impurities in the

sample.

6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0 1 1 0 0 1 2 0 0 1 3 0 05 0

3 0 0

5 5 0

8 0 0

1 0 5 0

1 3 0 0

1 5 5 0

1 8 0 0

Photo

lumine

scen

ce (c

ounts

/s)


3 k W / c m 2

1 0 . 2 k W / c m 2

1 2 . 5 k W / c m 2

1 7 k W / c m 2

Figure 7.14: A PL spectrum at 2.2× 10−4 mbar. Increasing the laser intensity reducesthe fluorescence count. At higher laser intensity, the spectrum showed anadditional emission band between 750 nm and 1050 nm. This increased withlaser intensity, and is probably related to impurities in the sample.

Reducing the pressure decreases the PL count rate until saturation point is reached.

A further increase in laser intensity quenches the fluorescence, probably due to in-

creased temperature of the diamond. The background gas acts as a heatsink, so that,

at lower pressures, the internal temperature increases, thus increasing the probabil-

ity of non-radiative transitions.

From Fig 7.11, we can see that equation 7.2 agrees with the PL saturation curve at

atmospheric pressure, but does not describe the PL intensity in vacuum, where it

(the PL intensity) starts to decline at high laser intensities. We found that the pho-

112

toluminescence intensity IPL could be described as a function of the laser intensity

L by the third degree polynomial:

IPL(L) =C0 +C1L+C2L2 +C3L3, (7.3)

where C0 = 0 is the intersect, set at 0 count/s (no PL at zero laser intensity), and

C1, C2 and C3 are the coefficients in the polynomial fit, listed in table 7.3. Note

that derivative of this cubic function shows how photoluminescence intensity varies

with laser intensity as shown in table 7.4.

Table 7.3: Coefficients in the polynomial fit for the saturation curves in Fig 7.11.

Pressure C1 C2 C3

(mbar)(

kCountss · cm2

kW

) (kCounts

s · cm4

kW2

) (kCounts

s · cm8

kW3

)Atmospheric 836 ± 22 -15 ± 5 -0.2 ± 0.24.5×10−1 631 ± 17 -14 ± 3 -1.1 ± 0.12.2×10−4 684 ± 37 -62 ± 12 0.3 ± 0.9

Table 7.4: Variation of the photoluminescence intensity with the laser intensity at differentpressure levels.

Laser intensity IPL(kCounts

s

)(kWcm2

)Atmospheric 4.5×10−1 mbar 2.2×10−4 mbar

1 806 601 5613 742 521 3205 673 415 889 523 126 -35410 483 38 -13 356 -264 -15 266 -498 -

To sum up, we have demonstrated that, at high laser intensity and under vacuum

conditions, the emission of NV− is significantly decreased. The observed spec-

trum showed that this decrease is not related to the charge state conversion of the

NV centre. We have also shown that the theoretical curve given by the equation

IPL(L) = I∞(L

L+Lsat) fits well to the PL saturation curve at atmospheric pressure,

113

but does not describe it well in vacuum, particularly at high laser intensities. We

found that the PL saturation curves can be described by a cubic function at any pres-

sure level. The heat generated from the absorption of laser radiation is expected to

quench the fluorescence, especially under vacuum. This rise in internal temperature

rise will increase the probability of non-radiative transitions, and can be estimated

by ODMR measurement, as we will describe in the next section.

7.9 ODMR spectrum under different vacuum levelsAs described in the previous section, lower pressures lead to reduced PL intensity.

This is probably a result of temperature-induced non-radiative quenching, which

increases the probability of transitions through the dark state. In this section, we

will investigate the effect of tempreture changes on the ODMR spectrum. As de-

scribed in section 2.5, other studies have shown that the ODMR peak changes with

temperature. This will allow us to determine temperature changes as a function of

shift in ZFS. To do this, the ODMR spectrum was recorded at atmospheric pressure

as shown in Fig 7.15. This was repeated using different laser intensities, in order

to increase the temperature of the diamond lattice. The results are shown in Fig

7.16 and table 7.5. We can see that, initially, the ODMR contrast increased with

increasing the laser intensity, peaking at 3 kW/cm2. At higher laser intensities, the

ODMR contrast decreased again, as expected. However, the ZFS frequency de-

creases with all increasing laser intensities. Below pressures of 4.5× 10−1 mbar,

temperature changes were greater, as can be seen in Fig 7.17. This was attributed

to the the reduction in surrounding gas, which removes heat. The fitted ODMR

spectrum shows that contrast decreased with increasing laser intensity (Fig 7.17

and table 7.6), and the ODMR dip was shifted considerably, compared with atmo-

spheric pressure (Fig 7.18). For example, at a laser intensity of 8 kW/cm2, the

ESR frequency at atmospheric pressure was 2.865 GHz, while it was 2.851 GHz at

4.5×10−1 mbar. This shift (14 MHz) is about half the peak width.

To further investigate the effect of high vacuum conditions, the pressure was re-

duced to 2.2× 10−4 mbar. The recorded ODMR spectra are shown in Fig 7.19.

114

Note that, the increases in temperature of the sample, as a result of increasing the

laser intensity, varies with pressure. As we can see from Fig 7.20, the tempera-

ture was raised significantly. The contrast reduced dramatically with a large shift in

the ESR frequency (the ESR frequency was about 2.83 GHz at a laser intensity of

8 kW/cm2, which is a shift of 35 MHz from the frequency at atmospheric pressure).

At laser intensities higher than 8 kW/cm2, it was hard to detect the ODMR dip.

2 . 7 9 2 . 8 2 2 . 8 5 2 . 8 8 2 . 9 1 2 . 9 4

0 . 8 50 . 8 80 . 9 10 . 9 40 . 9 71 . 0 0

Norm

alize

d PL c

ount

0 . 5 k W / c m 2 1 k W / c m 2

0 . 8 50 . 8 80 . 9 10 . 9 40 . 9 71 . 0 0

Norm

alize

d PL c

ount

3 k W / c m 2 5 k W / c m 2

2 . 7 9 2 . 8 2 2 . 8 5 2 . 8 8 2 . 9 1 2 . 9 40 . 8 50 . 8 80 . 9 10 . 9 40 . 9 71 . 0 0

Norm

alize

d PL c

ount


8 k W / c m 2


1 1 k W / c m 2

Figure 7.15: ODMR spectra at atmospheric pressure with varying laser intensity. The datawas fitted using a Lorentzian function. The ESR frequency decreases withincreasing laser intensity. The ODMR contrast, however, increased initially,but peaked up at 3 kW/cm2, then decreases at higher laser intensities. Allvalues are shown in table 7.5.

115

Table 7.5: ZFS frequency and ODMR contrast obtained from Fig 7.15.

Laser Intensity (kW/cm2) ZFS Frequency (GHz) ODMR Contrast (%)0.5 2.8732 ± 0.0006 9.82 ± 0.291 2.8682 ± 0.0004 10.45 ± 0.223 2.8660 ± 0.0003 11.70 ± 0.165 2.8658 ± 0.0003 11.21 ± 0.168 2.8647 ± 0.0003 10.48 ± 0.15

10 2.8641 ± 0.0003 9.43 ± 0.12

0 2 4 6 8 1 02 . 8 6 4

2 . 8 6 6

2 . 8 6 8

2 . 8 7 0

2 . 8 7 2

2 . 8 7 4

Frequ

ency

(GHz

)

L a s e r i n t e n s i t y ( k W / c m 2 )

Figure 7.16: ZFS frequency for various laser intensities, at atmospheric pressure. The fre-quencies were obtained from the ODMR spectrum in Fig 7.15. The shift ofZFS frequency was about -9 MHz over the entire range.

116

Figure 7.17: ODMR spectra at 4.5× 10−1 mbar for different laser intensities. The ZFSfrequency and contrast decreased with increasing laser intensity. By reducingthe pressure, the heat transfer rate between the sample and the surroundinggas was decreased, resulting in a large shift in the ZFS frequency. All valuesare shown in table 7.6.

117

Table 7.6: ZFS frequency and ODMR contrast obtained from Fig 7.17.

Laser intensity (kW/cm2) ZFS frequency (GHz) ODMR contrast (%)0.5 2.8662 ± 0.0008 11.65 ± 0.363 2.8627 ± 0.0004 11.70 ± 0.195 2.8590 ± 0.0005 10.56 ± 0.208 2.8518 ± 0.0005 9.55 ± 0.20

10 2.8452 ± 0.0004 8.47 ± 0.2012.5 2.8370 ± 0.0006 5.49 ± 0.1914 2.8303 ± 0.0007 4.05 ± 0.1715 2.8240 ± 0.0009 3.16 ± 0.17

0 2 4 6 8 1 0 1 2 1 4 1 62 . 8 2 5

2 . 8 3 5

2 . 8 4 5

2 . 8 5 5

2 . 8 6 5

2 . 8 7 5

Frequ

ency

(GHz

)


Figure 7.18: The ZFS frequency for various laser intensities at 4.5× 10−1 mbar. The fre-quencies were obtained from the ODMR spectrum in Fig 7.17. The shift inZFS frequency was about -42.2 MHz over the entire range.

118

0 . 8 4

0 . 8 8

0 . 9 2

0 . 9 6

1 . 0 0

Norm

alize

d PL c

ount

0 . 5 k W / c m 2 3 k W / c m 2

2 . 7 9 2 . 8 2 2 . 8 5 2 . 8 8 2 . 9 1 2 . 9 40 . 8 4

0 . 8 8

0 . 9 2

0 . 9 6

1 . 0 0

Norm

alize

d PL c

ount


5 k W / c m 22 . 7 9 2 . 8 2 2 . 8 5 2 . 8 8 2 . 9 1 2 . 9 4


8 k W / c m 2

Figure 7.19: ODMR spectra at 2.2×10−4 mbar for different laser intensities. The ZFS fre-quency and contrast decrease with increasing laser intensity. The temperatureincreased significantly due to the reduction in the surrounding gas, which actsas a heatsink. All values are shown in table 7.7.

Table 7.7: ZFS frequency and ODMR contrast data from Fig 7.19.

Laser Intensity (kW/cm2) ZFS Frequency (GHz) ODMR Contrast (%)0.5 2.8660 ± 0.0013 8.37 ± 0.543 2.8512 ± 0.0008 6.93 ± 0.265 2.8590 ± 0.0007 6.69 ± 0.218 2.8294 ± 0.0008 4.92 ± 0.18

119

0 2 4 6 82 . 8 2 5

2 . 8 3 5

2 . 8 4 5

2 . 8 5 5

2 . 8 6 5

2 . 8 7 5

Frequ

ency

(GHz

)


Figure 7.20: The ZFS frequency for various laser intensities at at 4.5× 10−1 mbar. Thefrequencies were obtained from the ODMR spectrum in Fig 7.19. The shift inZFS frequency was about -36.6 MHz over the entire range.

7.10 Temperature dependence of ZFSIn previous sections, we have demonstrated that a decrease in pressure quenches

NV photoluminesence and reduces the ODMR contrast with a shift of the ZFS fre-

quency. This is probably a result of the increased temperature of the NV diamond

when it is exposed to the 532 nm excitation laser. The temperature dependence of

ZFS has been previously studied. These models are grouped into three different

temperature regions, based on how the zero field splitting varies [49, 50, 52].

In the low temperature region from 5.6 K to 295 K, ZFS changes with temperature

are described by a fifth degree polynomial. The change in ZFS is about 7 MHz (from

2.877 GHz to 2.87 GHz) in this temperature range [50]. In the middle temperature

region, between 280 K and 330 K [49], ZFS varies linearly with temperature but

with a negative slope equal to dD/dT =-74.27 kHz/K, where D represents the ZFS

frequency. Third, in the high temperature region from 300 K to 700 K, the variation

of D with temperature is described by a cubic polynomial function with a thermal

120

shift that varies from dD/dT =-80 kHz/K at 300 K up to dD/dT =-170 kHz/K at

700 K. The shift in D between these two temperatures is about -56 MHz [52].

From these three regions we can see that D(T ) shifts up from 2.87 GHz when the

temperatures is below 300 K, and shifts below 2.87 GHz when the temperature is

higher than 300 K.

Our measurement in the previous section shows that the ZFS frequency shifts below

2.87 GHz when we increase laser intensity, at either atmospheric pressure or under

vacuum. This decrease in the ZFS frequency indicates that we are operating in the

high temperature region discussed above, and that the temperature is above 300 K.

The ZFS frequency parameter denoted as D in this region is described by a cubic

polynomial function given by [23, 52]:

D(T ) = a0 +a1T +a2T 2 +a3T 3 +∆pressure +∆strain, (7.4)

where a0 = (2.8697 ± 0.0009) GHz, a1 = (9.7 ± 0.6) × 10−5 GHz/K,

a2 = (−3.7± 0.1)× 10−7 GHz/K2, a3 = (1.7± 0.1)× 10−10 GHz/K3, ∆strain is

the change in D caused by the local strain, which ranges between 2 to 9 MHz [37],

and ∆pressure = 1.5 Hz/mbar is the linear shift of D with pressure [53].

Note that reducing the pressure from atmospheric pressure to 2.2×10−4 mbar leads

to a slight temperature rise of approximately 11 mK above room temperature. How-

ever, this is negligible in comparison with the temperature change associated with

the total shift in D and the uncertainty in equation 7.4, which is about ±20 K. From

this cubic function, we could derive the temperature from the corresponding shift of

ZFS frequency measured in the previous section. As a first step, we used equation

7.4 to determine the temperature dependence of the laser intensity as shown in Fig

7.21. The linear fit intersects with the temperature axis (laser intensity = 0) around

320±20 K. This was higher than the expected value, which should be around room

temperature at zero laser intensity. From this temperature difference, we can esti-

mate the shift in D due to the strain, which was found to be about 2 MHz. We can

also obtain the coupling parameters between temperature and laser intensity from

the linear regression slope in Fig 7.21. These parameters are listed in table 7.8.

121

Table 7.8: Coupling parameters between temperature and laser intensity.

Pressure (mbar) dTdL

(Kcm2

kW

)1×103 4.88 ± 0.45

4.5×10−1 20.34 ± 0.432.2×10−4 41.13 ± 2.22

1 3 5 7 9 1 1 1 3 1 52 5 03 0 03 5 04 0 04 5 05 0 05 5 06 0 06 5 07 0 0

Temp

eratur

e (K)


Figure 7.21: Temperature dependence of laser intensity at different pressure levels. Theblack dots represent the data at atmospheric pressure, the blue dots at4.5× 10−1 mbar and the green dots at 2.2× 10−4 mbar. The solid line rep-resents a linear fit of the data. All linear fits intersect the temperature axisaround 320±20 K.

As the frequency shift due to the local strain has been determined, equation 7.4 can

be used to calculate the temperature from the ZFS frequency as shown in Fig 7.22.

For a given laser intensity, lowering the pressure decreases the heat transfer rate be-

tween the NV diamond and the surrounding gas. From Fig 7.23, we can determine

the temperature at fixed laser intensities for three different pressure levels. For ex-

ample, at a laser intensity of 8 kW/cm2, the ZFS frequency shifts of about -35 MHz

from atmospheric pressure down to 2.2×10−4 mbar, which raises the temperature

by 247 K.

122

2 . 8 22 . 8 32 . 8 42 . 8 52 . 8 62 . 8 72 . 8 8

2 . 8 22 . 8 32 . 8 42 . 8 52 . 8 62 . 8 72 . 8 8

2 4 0 3 0 0 3 6 0 4 2 0 4 8 0 5 4 0 6 0 0 6 6 0 7 2 02 . 8 22 . 8 32 . 8 42 . 8 52 . 8 62 . 8 72 . 8 8

Frequ

ency

(GHz

) 1 0 0 0 m b a rFre

quen

cy (G

Hz) 4 . 5 ´ 1 0 - 1 m b a r

Frequ

ency

(GHz

)

T e m p e r a t u r e ( K )

2 . 2 ´ 1 0 - 4 m b a r

Figure 7.22: Deduced temperature from ZFS at different pressure from a change in laserintensity. The red line represents the cubic polynomial fit of the data points.The temperature is derived from the ZFS frequency using equation 7.4. In-creasing the laser intensity from 0.5 kW/cm2 to 8 kW/cm2 leads to a ZFS fre-quency shift about -8.5 MHz at 1000 mbar, -14.4 MHz at 4.5×10−1 mbar and-37 MHz at 2.2×10−4 mbar. This raises the temperature by 92 K, 116 K and259 K respectively.

123

1 3 5 7 9 1 1 1 3 1 5

2 . 8 2 02 . 8 2 52 . 8 3 02 . 8 3 52 . 8 4 02 . 8 4 52 . 8 5 02 . 8 5 52 . 8 6 02 . 8 6 52 . 8 7 02 . 8 7 5

6 8 06 5 16 2 15 9 05 5 95 2 74 9 34 5 74 1 83 7 53 2 52 5 8

Frequ

ency

(GHz

)

Temp

eratur

e (K)


Figure 7.23: Comparison of the ZFS frequency and corresponding temperature from achange in laser intensity at different pressure levels. The black dots rep-resent the data at atmospheric pressure, the red dots represent the data at4.5× 10−1 mbar, the blue dots represent the data at 2.2× 10−4 mbar. Theerror bars show the uncertainty in frequency. The temperature axis is calcu-lated using equation 7.4 for each corresponding frequency. Lower the pres-sures probably decrease the heat transfer rate between the NV diamond andthe surrounded gas, which increases the temperature of the diamond lattice.The result is a large shift in ZFS frequency. Between atmospheric pressureand 2.2× 10−4 mbar, the temperature was increased by 119 K at 3 kW/cm2,191 K at 5 kW/cm2 and 247 K at 8 kW/cm2.

7.11 ODMR contrastAs discussed in section 7.9, the temperature change not only affects the reso-

nance frequency but also the ODMR contrast. Based on temperatures correspond-

ing to ZFS frequency, we can draw a relationship between the temperature and

ODMR contrast. It can be seen from Fig 7.24 that, by increasing laser intensity to

3 kW/cm2, the contrast increases from 9.8% to about 11.7%. The temperature at

3 kW/cm2 was about 366 K. At higher laser intensities, the contrast starts to de-

crease until it reachs 9.43% at 384 K, where the laser intensity was 10 kW/cm2. Un-

der vacuum, the contrast slightly increases between laser intensities of 0.5 kW/cm2

124

to 3 kW/cm2, peaking at 11.7%. It then falls with temperature down to 3− 5% as

seen in Fig 7.25 (at 4.5×10−1 mbar) and Fig 7.26 (at 2.2×10−4 mbar).

2 6 0 2 8 0 3 0 0 3 2 0 3 4 0 3 6 0 3 8 0 4 0 09 . 0

9 . 5

1 0 . 0

1 0 . 5

1 1 . 0

1 1 . 5

1 2 . 0OD

MR Co

ntras

t (%)


Figure 7.24: Effect of temperature change on ODMR contrast at atmospheric pressure. TheODMR contrast was 9.8% at room temperature, peaking at 11.7% at 366 K.It then decreased to 9.43% at 384 K.

3 2 0 3 6 0 4 0 0 4 4 0 4 8 0 5 2 0 5 6 0 6 0 0 6 4 0 6 8 02

4

6

8

1 0

1 2

ODMR

Contr

ast (%

)


Figure 7.25: The effect of temperature change on ODMR contrast at 4.5×10−1 mbar. TheODMR contrast was 11.7% at 396 K down to 3.2% at 657 K.

125

3 2 0 3 6 0 4 0 0 4 4 0 4 8 0 5 2 0 5 6 0 6 0 0 6 4 0 6 8 04

5

6

7

8

9

1 0

ODMR

Contr

ast (%

)


Figure 7.26: The effect of temperature change on ODMR contrast at 2.2×10−4 mbar. TheODMR contrast fell from 8.4% at 366 K to 5% at 625 K.

In summary, from the observed measurements, the ODMR contrast reached its peak

at about 380±35 K by using 3 kW/cm2 of laser intensity at atmospheric pressure

and 4.5×10−1 mbar. It then fell, due to the PL saturation associated with increased

probability of non-radiative transition.

7.12 ConclusionIn this chapter we demonstrated optically detected magnetic resonance (ODMR) of

NV centres in diamond, placed in a linear quadrupole trap using a cost effective

detection set-up. We showed experimentally that using one of the linear trap elec-

trodes as a monopole antenna, as described in chapter 6, is feasible, and that the

power generated was sufficient for NV excitation. NV fluorescence from microdi-

amond was used to investigate how NV photoluminesence varies as a function of

laser intensity, temperature, and gas pressure. We found that, at high laser inten-

sities, the photoluminescence of NV− (the PL saturation curve) is quenched under

vacuum, due to the increased probability of non-radiative transition. We also found

that the reported theoretical expression for PL saturation, IPL(L) = I∞(L

L+Lsat), de-

scribes well the PL at atmospheric pressure but not in vacuum. A third degree

polynomial was shown to fit the PL saturation curve under any pressure level. The

126

quenching was a result of the increased temperature of the NV diamond, and can

be estimated by measuring the changes in resonance frequency. These measure-

ments showed that the NV diamond sample reached a temperature as high as 657 K

at 4.5× 10−1 mbar, with an ODMR contrast of 3.2%. The results also showed

that temperature increased by 247 K when lowering the pressure from atmospheric

pressure down to 2.2×10−4 mbar at a laser intensity of 8 kW/cm2. The results also

indicate that the contrast reduces when the temperature is higher than 380±35 K.

The findings reported in this chapter therefore provide the fundamentals of how

temperature changes due to laser intensity and pressure can drive the non-radiative

decay and influence the photoluminesence properties significantly. This will be an

important aspect when considering the use of NV diamond to carry out the macro-

scopic matter-wave experiments, as optical readout of the spin state is based on the

PL intensity of the NV centres, which is used to evidence the spatial superposition.

It is important for this experiment to have fast MW pulses to manipulate the spin

state. These pulses should be tuned to a given frequency that is equal to the ZFS

frequency. As we showed in this chapter, this frequency will shift with the tem-

perature changes induced by the optical field. This means that before starting the

experiment, we must measure the ZFS frequency. This frequency should not change

during the experiment.

The results in this chapter have helped us to understand the effect of heating on pho-

toluminescence properties, especially under vacuum, which will be the main issue

for levitated NV diamond as will described in the next chapter.

Chapter 8

Observing NV photoluminescence in

the Paul trap

8.1 OverviewIn previous chapters, we have described the construction and characterisation of the

Paul trap, as well as the optical and microwave systems used to perform ODMR on

an NV nanodiamond. In this chapter, we describe the levitation of diamond particles

within the trap and its prospects for future in-trap matter-wave experiments.

8.2 Sample characteristicsIt was decided to begin trapping experiments with micro-diamond rather than nan-

odiamond, as it is easier to observe fluorescence. Initial experiments utilised 1 µm

diamond in powder form (from Columbus Nanoworks). A mixture of these par-

ticles with ethanol was introduced into the trap by a nebuliser (Omron MicroAir

NE-U22). However, though particles were easily trapped, no PL was observed. Ini-

tially, it was thought that this could be due to the presence of other particulates in

the powder supplied to us, so the PL spectrum of the samples was studied, using a

RENISHAW inVia Raman Microscope with 514 nm excitation. The samples avail-

able for trapping were 1 µm and 100 nm diamonds from Columbus Nanoworks in

powder form, and 100 nm particles from Adamas Nanotechnologies delivered as

1 mg/ml slurries in de-ionized (DI) water. The first sample examined was 1 µm

diamond, which as mentioned above, did not produce a detectable PL signal. The

128

nebuliser used for introducing the particles into the trap was also used to deposit the

particles on a microscope glass slide. This was done to determine whether we could

observe any NV PL from the glass slide, which should contain many more than

the single particle levitated in the trap. Several clusters of the same 1 micron size

diamonds deposited on the microscope slide, and the PL spectra was collected by a

10X microscopic objective. The resulting spectrum showed a broadened peak be-

tween 630 to 850 nm as seen in Fig 8.1, which is within the range of the broadened

peak usually observed in NV diamond. However, there was no peak for NV− ZPL

at 640 nm. Other diamonds, from different parts of the sample, showed a similar

spectrum to the first. From these spectra, we concluded that this batch of microdia-

monds probably does not contain NV centres. The broadened peak observed seems

very similar to the fluorescence from an empty glass slide, as can be seen from the

in Fig 8.2. The glass slide was therefore replaced with a quartz one. After this, the

spectra showed no signs of the glass fluorescence or the NV spectrum as shown in

Fig 8.3.

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0

2 0

4 0

6 0

8 0

1 0 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.1: PL spectra of 1 µm in diameter microdiamond particles from Columbus

Nanoworks. The particles were mixed with ethanol and then deposited ontoa microscopic glass slide using a nebuliser. The sample was placed under a10X microscope objective and the spectrum recorded using a 10 s exposuretime. The excitation laser intensity was 8.4 kW/cm2. The spectra has a broad-ened peak between 630 to 850 nm which could be related to NV spectrum.However, there was no peak for NV− ZFL at 640 nm, which suggested no NVwere in the sample. Inset is an image of the region examined, which is about1 µm in diameter.

129

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0

2 0

4 0

6 0

8 0

1 0 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.2: PL spectra of an empty microscope glass slide. The slide was examined us-

ing a 10X microscope objective and 10 s exposure time. The excitation laserintensity was 8.4 kW/cm2.

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 012345678

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.3: PL spectrum of 1 µm diameter microdiamond particles from Columbus

Nanoworks, deposited on a quartz slide by a nebuliser. The sample was ex-amined using a 10X microscope objective with a 10 s exposure time, ans alaser intensity of 13 kW/cm2. No NV spectrum was observed. The inset showsan image of the examined region, which is approximately 7.5 µm in diameter.

This next step was to assess whether the solvent used in the nebulisation process

affected the PL spectrum. To check this, a new sample, consisting of the same

particles, but in a powder form (not mixed with solvent), was deposited on a quartz

slide, and the PL spectrum recorded. This (Fig 8.4) showed a clear NV PL spectral

130

signature. This comparison of spectra (with and without solvent) led us to conclude

that this sample probably contained a significant level of impurities, and that, when

nebulised, only these impurities were deposited on the cover slide. The same results

were obtained for smaller sized (100 nm) diamond from the same supplier. This

suggested that it was not the nebulisation process that had been responsible for the

lack of NV PL.

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 01 0 03 0 05 0 07 0 09 0 0

1 1 0 01 3 0 01 5 0 0

Photo

lumine

scen

ce (c

ounts

/s)


Figure 8.4: PL spectrum of microdiamond particles from Columbus Nanoworks with anominal diameter of 1 µm. The particles, in powder form, were placed directlyon a quartz slide. The sample was placed under a 10X microscope objective. Aspectrum acquired with 13 kW/cm2 of laser intensity and 10 s exposure time.The results show a clear NV spectrum with a sharp NV− ZPL peak at 640 nm,indicating that the powder does contain NV centres. The inset shows an imageof the examined region, which has a diameter of about 1.75 µm.

Following this, a 100 nm nanodiamond solution (from Adamas Nanotechnologies)

was prepared. The particles had been pre-suspended in DI water. A 100 µg/100 µl

sample was drop-cast onto a quartz slide, and an NV PL spectrum acquired as seen

in Fig 8.5. First, however, as a nebuliser would be used to introduce the particles to

the trap, a mixture of these particles and ethanol was first nebulised onto the quartz

slid to see if any particles containing NV could be seen. Three different clusters

of diamonds deposited on the surface were studied. The first region showed no de-

tectable NV PL. The other two regions, however, showed a clear NV spectrum as

seen as an example in Fig 8.6. As we could clearly see spectra from the samples

from Adamas Nanotechnologies, they were selected for use in the levitated experi-

ments.

131

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0

3 06 09 0

1 2 01 5 01 8 02 1 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.5: PL spectrum from a 100 nm nanodiamond solution from Adamas Nanotech-

nologies delivered as 1 mg/ml slurries in DI water. A sample (100 µg/100 µl)was drop-cast onto a quartz slide. The spectrum was acquired under 50X mi-croscope objective with 10 s exposure time. The excitation laser intensity was4 kW/cm2. The result was a clear NV spectrum with NV0 ZFL at 575 nmand NV− ZFL at 640 nm. The inset shows the examined region, which has adiameter about 1.5 µm.

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0

5

1 0

1 5

2 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.6: PL spectrum from 100 nm nanodiamond (from Adamas Nanotechnologies) de-

livered as 1 mg/ml slurries in DI water. A mixture of these particles and ethanolwas nebulised into quartz slid. The spectrum was acquired using a 50X micro-scopic objective with 10 s exposure time. The excitation laser intensity was4 kW/cm2. The result was a clear NV spectrum with NV0 ZPL at 575 nm andNV− ZPL at 640 nm. The inset shows an image of the examined region, whichhas a diameter of about 4 µm.

Commercial NV diamond available for trapping, supplied by Columbus Nanoworks

and Adamas Nanotechnologies, was investigated. The sample from Columbus

132

Nanoworks had significant level of impurities, the nebulised mixture of these sam-

ple does not contain NV diamond. As the impurities could pass through the mesh

holes in the nebuliser, but not the larger NV diamond, the impurities were the only

component of the mixture that was nebulised. However, it was clear from the PL

spectra from the second sample (from Adamas Nanotechnologies) that had a smaller

proportion of impurities compared to the sample from Columbus Nanoworks. We

therefore selected the sample supplied by Adamas Nanotechnologies for the lev-

itated experiments since we could routinely load NV diamond into the trap and

observe a clear NV spectra.

8.3 NV photoluminescence from levitated diamondControlling the NV spin of levitated diamond has some experimental complexi-

ties. These complexities derive from the difficulty of observing and monitoring

the NV PL while it is levitated. For example, the Brownian motion of optically

levitated diamond in liquid or air can move the particles out of the observation re-

gion [93, 107, 108] especially at the low trap frequency of a Paul trap. Also, most

optically levitated nanodiamond using 1064 nm laser trapping shows no NV fluores-

cence [29]. Another issue is the burning, or graphitisation, of the levitated diamond

when measurements are made at near vacuum pressure (about 1 mbar) [54]. This

occurs due to the absorption of light from the trapping laser and the reduction in

heat transfer as the surrounding gas pressure is reduced. Replacing the optical trap

with an electrical trap should resolve this last issue, and Delord et al. [31] reported

the observation of NV fluorescence from 10 µm diamond at 2×10−2 mbar. How-

ever, a 532 nm excitation laser using 700 µW of laser power was still enough to heat

up the particle and cause trap loss. In our experiment, we successfully observed NV

fluorescence from levitated nanodiamond using the 100 nm samples from Adamas

Nanotechnologies. These particles was chosen based on the tests described in the

previous section. The experimental scheme is illustrated in Fig 8.7, where a mixture

of these particles and ethanol was nebulised into the trapping region of the linear

quadrupole trap. A CCD camera was used to observe the scattered light from the

133

levitated particle, which was collected by two 50 mm achromatic lenses (AL), with-

out using any filters. We trapped using 2 kVpeak−peak on the AC drive between 2 to

9 kHz with a 31 V endcap voltage. The secular frequency at atmospheric pressure

could not be measured due to air damping. We assumed that the trapped particle

had 100 nm diameter, and from the stability condition we expected a particle charge

in the range of 1×1.6×10−19 C≤ Q≤ 62×1.6×10−19 C. The CCD camera was

then replaced with an optical fibre connected to a spectrometer (Andor Shamrock

303i spectrograph with 1200 lines/mm grating and 40 nm bandpass). The fibre was

realigned to obtain the maximum intensity of scattered green (532 nm) light before

attempting to detect NV fluorescence. Here, fluorescence was filtered by a notch

filter centred at 532 nm (NF) and a long pass filter (LP) with a cut-off wavelength

of about 610 nm. The observed NV spectrum at a laser intensity of 57 kW/cm2 is

shown in Fig 8.8. The spectrum was recorded from 610 nm to 900 nm and accumu-

lated with an exposure time of 9.12 mins. Individual scans with a 40 nm bandpass

were merged to cover the whole wavelength range. The variable voltage on the

endcap electrodes allowed us to align the particle and maximise the fluorescence

signal. It also allowed us to translate the trapped particle away from the collection

lens focal point to detect the background signal as seen in Fig 8.8. This gave us

the ability to measure the background without having to drop the particle. This will

be a useful feature, allowing us to subtract the background when the laser power

is changed or when using another laser to cool the internal temperature of NV dia-

mond coating with Yb3+:YLF crystals. Also, this feature could overcome the issue

reported by Delord et al. [31], where levitating the micro-diamond in a ring trap

shifted it from the trap centre due to the effect of the damping rate on the secular

frequency. It should be noted that during the acquisition, the strong background

signal could make detection of the NV spectrum difficult, as seen in Fig 8.9. This

noise was not apparent when the 532 nm laser was off and is most likely produced

by unwanted fluorescence from optical components along the laser optical axis.

134

Vacuum chamber

PumpVacuum

gauge

Optical fibre

Collimator Optical fibre to

APD or spectrometer

MW

NF LPF

ALAL

AC

ACGND

GND

&

MW

CCD

camera

Figure 8.7: Schematic of the levitating experiment set-up. A mixture of 100 nm nanodi-amond particles and ethanol was nebulised into the trapping region of the lin-ear quadrupole trap. An optical fibre connected to a collimator was used for532 nm laser excitation. The optical detection set-up consisted of two 50 mmachromatic lenses (AL) to collect the light. A CCD camera was used to viewthe levitated particle. For fluorescence detection, an optical fibre attached to anAPD or spectrometer was used, after filtering the fluorescence by a notch filtercentred at 533 nm (NF) and a long pass filter (LP) with cut-off wavelength ofabout 610 nm.

6 4 0 6 8 0 7 2 0 7 6 0 8 0 0 8 4 0 8 8 00

1 0

2 0

3 0

4 0

5 0

6 0

7 0

Photo

lumine

scen

ce (c

ounts

/s)


N V s p e c r u m A f t e r r e a l i g n m e n t b y e n d c a p s O u t o f s p o t

Figure 8.8: NV spectrum of levitated diamond. The laser intensity was set at 57 kW/cm2

and spectra were accumulated twice and recorded from 610 nm to 900 nm.The exposure time was 34.16 s with a total acquisition time of 9.12 mins. Theendcap electrode voltage was used to improve the signal by shifting the particletoward the focal point of the collective lens or moving it away to obtain thebackground signal. This could be changed by tuning the endcaps voltage.

135

6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 002 04 06 08 0

1 0 01 2 01 4 01 6 01 8 0

Photo

lumine

scen

ce (c

ounts

/s)


Figure 8.9: An NV spectrum of a levitated diamond before and after subtracting the back-ground. The green line represents the spectrum before subtracting the back-ground, the black line represents the background and the red line representsthe spectrum after subtracting the background. The laser intensity was set at57 kW/cm2 and the exposure time was 34.16 s with total acquisition time of9.12 mins. The background noise signal was approximately 71% of the signalcount.

8.4 Background noiseThe background noise must be as low as possible during the acquisition. As men-

tioned in the previous section, a background signal was found when the 532 nm laser

was turned on without trapped nanodiamond. This was probably a result of fluores-

cence from optical components, such as windows, and other trap elements along the

laser optical axis. We therefore removed the windows, but observed no consequent

reduction in the background spectrum. We then investigated other components of

the trap. The primary materials used to build the trap are stainless steel (for the AC

and endcap electrodes) and nylon (for the spacers). Using the same process as in

section 8.2, the trap components were examined by recording spectra with a Raman

microscope using 514 nm excitation. The previously-observed background spec-

tra had two broadened peaks, one between 690 nm to 750 nm, and the other from

750 nm to 825 nm (Fig 8.10), while the PL spectrum of the stainless steel electrodes

had an emission band spectrum centred at about 647 nm (Fig 8.11). As this was not

observed in the background spectrum, we conclude that the electrodes do not add to

the spectral background. Similarly, by examining the emission spectra of the nylon

136

spacers (Fig 8.12), we can see that the spectra appear at a shorter wavelength than

that of the background emission and are, therefore, also not an important source of

background in our measurements.

6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 00

2 0

4 0

6 0

8 0

1 0 0

1 2 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.10: The background spectra obtained from the levitated diamond experiment. The

laser intensity was 57 kW/cm2 and the exposure time was 34.16 s, with atotal acquisition time of 9.12 mins. The spectrum has two broadened peaksbetween 690 nm to 750 nm, and 750 nm to 825 nm.

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 0

5

1 0

1 5

2 0

2 5

3 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.11: PL spectrum of the stainless steel electrodes used for the AC and endcap elec-

trodes, obtained using a 50X microscope objective and a 20 s exposure time.The laser intensity was 39.5 kW/cm2. The spectrum has a broadened emissionband centred at about 647 nm.

137

5 5 0 6 0 0 6 5 0 7 0 0 7 5 0 8 0 0 8 5 0 9 0 05 0

1 5 0

2 5 0

3 5 0

4 5 0

5 5 0

6 5 0

Photo

lumine

scen

ce (c

ounts

/s)

W a v e l e n g t h ( n m )Figure 8.12: PL spectrum of the nylon spacer, obtained using a 50X microscope and 20 s

exposure time. The laser intensity was 39.5 kW/cm2. The emission band wasbelow 625 nm which is not in the range of the background peaks.

We conclude that neither of the trap components, nor the windows (which are made

of quartz) are the source of the background. The background fluorescence is there-

fore probably produced by optical components such the optical fibre, notch filter,

long pass filter and achromatic lenses lying along the detection axes. These com-

ponents are made from various type of glasses, and Schartner et al. [109] reported

the observation of a background fluorescence using a 532 nm laser for a various

type of glasses, such as LLF1 which is commonly used to make optical fibres. Ac-

cording to Schartner et al., the emission band of these glasses is between 700 to

900 nm as seen in Fig 8.13. This is within the NV emission band spectrum and

the background emission range measured in our investigation. Each optical com-

ponents used could contain any of these glasses (with a different structure, depends

on the manufacturer). In our case, we could not define the glass structure for each

optical component as the manufacturer does not provide a detailed description of

the materials used.

138

Figure 8.13: PL spectra for various type of glass using a 532 nm laser with a laser powerof 25 mW, adapted from Schartner et al. [109].

Although we cannot avoid using optical lenses and filters, we can reduce the effect

of the background noise by improving the NV fluorescence signal. This weak NV

signal can be improved by replacing the two achromatic lenses that are 150 mm

away from the trapped particle (N.A. less than 0.25) with a high N.A. lens closer

to the particle. This will improve the poor light collection of the detection set-up.

This change (a lens near the trap inside the vacuum chamber) could be considered

as part of a re-engineered version of the system for future experiments.

8.5 LimitationsIn this section, we describe a few practical details that have limited observation of

the NV spectrum, which need to be taken into account to improve the experiment.

The first limitation is background emission, which contributes about 70% of the

total acquisition count. This limited the observation of the NV spectrum, especially

when performing the ODMR measurements using an APD. All components along

the optical axis of the laser were examined to verify the source of this background

noise. We found that neither the trap components nor the vacuum window flanges,

which can be changed, were the source of this background. We assumed, therefore,

that the optical filters and lenses were the source of this background fluorescence.

139

8.6 ConclusionIn this chapter, we examined the observation of NV photoluminesence from levi-

tated 100 nm diameter nanodiamond at atmospheric pressure. We also demonstrated

that the loading process using a nebuliser preferentially deposits impurities over the

diamonds. The fluorescence from these impurities increases background count, es-

pecially under vacuum as seen in the previous chapter. We measured a significant

background to the NV photoluminesence and determined that fluorescence from the

trap components did not contribute to the background. It is likely that the optical

components used in the detection system are the source of this background, as most

glasses have fluorescence emission within the range of the NV spectrum.

We conclude from this study, and from the temperature dependence study in the

previous chapter, that a purer diamond sample will be essential for carrying out

the matter-wave interferometry proposal. This sample should have a lower level of

embedded defect impurities and less amorphous carbon on the surface, to reduce

light absorption and consequent heating [110]. This will help to avoid fluorescence

quenching, especially under vacuum where the internal temperature of the diamond

increases up to 700 K. In addition, the weak NV signal, due to the low N.A. im-

posed by the trap electrodes, needs to be improved by using a different trap design.

Addressing these limits will improve the signal-to-noise ratio, which is expected to

be low for the single NV emitter nanodiamond required for the matter-wave inter-

ferometry experiment.

Chapter 9

Conclusion and future work

This thesis describes the development of an experimental platform for exploring re-

cent theoretical proposals for creating macroscopic spatial superposition using lev-

itated nano diamond containing nitrogen vacancy centres (NV) [21]. A method for

electrodynamic levitation of nanodiamond has been demonstrated as well as a sys-

tem for measuring NV fluorescence and manipulation of NV spin. The feasibility

and limitations of this system for experiments in macroscopic quantum mechanics

have been explored.

9.1 Summary of current workIn the first part of this thesis, the dynamics and trapping principles of Paul traps was

reviewed, with an outline of the properties of the nitrogen vacancy centre relevant

to matter-wave interferometry. A range of electrical trap geometries were studied,

to determine their suitability for diamond levitation. Appropriate designs, with a

deep potential well and good optical access for efficient detection of NV fluores-

cence were considered. Of several established designs, a linear quadrupole trap was

chosen. Two different traps of this type were constructed and tested at atmospheric

pressure and under vacuum. The first, a cost effective trap, was constructed from a

printed circuit board. This was easy to fabricate and had a larger numerical aperture

for enhancing signal detection. Although not eventually used in this work, it has

since found application in other levitation experiments in the laboratory. A second

trap, used in most of the work in this thesis, was of a conventional linear Paul trap

141

design with cylindrical electrodes. This trap was designed with an integrated mi-

crowave antenna for excitation of NV centres. This antenna was also one of the

Paul trap electrodes. The magnetic field strength and the energy density of the mi-

crowave field within the trap was modelled, and it was found that the average power

density at the trap centre was affected by the trap electrodes and was 26% lower

than the power density calculated for a single MW antenna electrode. We demon-

strated that the MW antenna radiated sufficient power for NV excitation suitable for

an ODMR experiment.

In the second part of this thesis, a simple and cost effective system for optically

detected magnetic resonance (ODMR) of NV diamond was developed. NV fluo-

rescence from microdiamond was used to investigate the dependence of NV photo-

luminescence as a function of temperature, laser intensity and gas pressure. It was

found that the temperature change, induced by the absorption of laser light, not only

affected the resonance frequency but also the ODMR contrast. The contrast peaked

at about 11.7±0.2 % at 380±35 K down to 3.2±0.2 % at 657±20 K. This was

observed as a resonance frequency shift below the zero field splitting (at 2.87 GHz)

with more than 42 MHz. Finally, we successful observed NV fluorescence from

levitated nanodiamond at atmospheric pressure.

9.2 Future workFor the proposed matter-wave interferometry experiment, it is essential to levitate

a NV nanodiamond under high vacuum, manipulate the spin and then readout the

spin state at the end of the protocol. In this work, we demonstrated the ability to

trap 100 nm diamond down to 4×10−3 mbar and observed NV photoluminesence

at atmospheric pressure. We also demonstrated that readout of the spin was affected

by temperature changes in the diamond due to laser induced heating at different

pressures. We found that the temperature could reach 700 K for commercial NV

diamond which will quench NV photoluminesence. This is especially important in

vacuum where heat conduction by air is low. This issue of heating has so far been

a barrier toward implementing the matter-wave experiment using optically levitated

142

NV diamond [54, 110].

In the near term, addressing this heating issue is of central importance. Using

purer diamond will help to avoid photoluminesence quenching. Morley et.al [110]

demonstrated this by using a purer milled chemical vapour deposition (CVD) nan-

odiamond. This milled CVD diamond is approximately 1000 times purer than the

commercial NV diamond used in our experiment. These pure CVD nanodiamonds

can be optically trapped with laser intensities up to 700 GW/m2 at pressures of

5 mbar and shows no heating above room temperature. Using such nanodiamonds in

a Paul trap (as opposed to an optical trap) will improve matters still further as a Paul

trap does not require such a high optical intensity. Purer diamond has yet another

advantage in that it has a longer decoherence time, T2, which determines the period

over which any experiment can be undertaken. This time could be further increased

by reducing the concentration of embedded NV centres to prevent any spin-spin

interaction between NVs [48]. A longer T2 will also help to reduce the microwave

power required for exciting NV nanodiamonds. However, the purity level required

to prevent heating of levitated NV diamond is yet to be determined. For future

experiments, it is possible to determine whether the purity is sufficiently high by

carrying out ODMR measurements under vacuum, as undertaken in chapter 7. This

provides an indication of the extent to which the optical field induces heating of pure

NV diamond at different pressures. Additional work is also required to evaluate

whether T2 for levitated NV diamond is as long as for non-levitated NV diamond.

Vamivakas et al. [111] reported that T2 is unaffected for optically levitated 100 nm

nanodiamond with a single NV centre at atmospheric pressure, and at 25 mbar.

These experiments used a 1064 nm trapping laser with a power up to 195 mW,

and a 1.8 mW exciting optical field. Vamivakas et al. found that the internal tem-

perature is slightly increased above the room temperature, with a reduction in PL

intensity, but there was no effect on T2. However, behaviour under ultra high vac-

uum conditions, at respectively higher temperatures, has not yet been explored.

Another feasible approach to overcoming the heating issue is by cooling the inter-

nal temperature of NV diamond using Yb3+:YLF nanoparticles. These nanocrystals

143

could be cooled from 300 K to 130 K by using 1031 nm light [112]. Coating the

NV diamond with Yb3+:YLF crystals could act as a heat-bath and help to control

the internal temperature. Attaching the Yb3+:YLF particles to the nanodiamond

could be achieved by using a segmented linear quadrupole trap. Benson et al. [113]

reported a method to electrostatic coupling of two levitated particles in a segment

linear quadrupole trap as seen in Fig 9.1. Two particles with opposite charges were

levitated at each end of the segmented trap, and the segmented DC electrodes were

used to push the two particles toward each other. The Coulomb force resulting from

their opposite polarity pulled them together to form a larger crystal.

AC

GND GND GND

GND GND GND

+

+

+

++ -

- -

- -

AC

GND GND GND

GND GND GND

+

+

+

++-

+ -

+ -

AC

GND GND GND

GND GND GND

+

+

+

++

-

-+

-

-

Tim

e e

volu

tio

n

Figure 9.1: Schematic of a segment linear quadrupole trap reported by Benson et al. [113].The trap consist of four parallel cylindrical rods, two of the opposing rods areconnected to an AC voltage while the segmented rods are connected to ground(GND) or DC voltage, where the + and - represent the polarity of the DC seg-ments and the particles. This result in a potential well which separates eachcharged particle in the trap. When the polarity of the segments is changed, theparticles move along the trapping axis, as a result of electrostatic attraction.The two particles at the end form a larger particle.

The next important aspect is that NV− spins do not rotate when levitated inside

a Paul trap. Any rotation of the levitated particle will change the NV orientation,

which needs to be fixed during the experiment to perform the ODMR measure-

ments. Delord et al. [42], for example, reported that the radiation pressure of a

low intensity NV optical excitation field induces rotational motion of <2 µm size

trapped NV diamond inside a Paul trap. This motion occurs using 100’s of µW of

144

exciting optical field [42]. One possible solution is to deposit magnetic material on

the NV diamond and use a magnetic field to align the particle [43]. For this ap-

proach, it is important to ensure that the process does not lead to heating as a result

of additional laser light absorption from the magnetic material.

This thesis has explored some aspects of the trapping and manipulation of NV dia-

mond spin that can be utilised for the proposed matter-wave interferometry exper-

iment. However, it has shown that there are yet many experimental and technical

issues that need to be resolved before this exciting experiment can be realised.

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