Physics of Atomic clocks - sps.ch · G. Mileti, Engelberg, 6.3.2007 Laboratoire Temps - Fréquence-5-Essential Bibliography • Jacques Vanier, Claude Audoin, “The Quantum Physics

G. Mileti, Engelberg, 6.3.2007Laboratoire Temps - Fréquence - 1 -

Physics of atomic clocks

Gaetano Mileti

Laboratoire Temps – Fréquence (LTF)

(http://www2.unine.ch/ltf)

Institut de MicrotechniqueUniversité de Neuchâtel


Laboratoire Temps – Fréquence (LTF)

newly created on February 1st 2007

(http://www2.unine.ch/ltf)

Rue A. L. Breguet 1(c/o Institut de Physique)Institut de MicrotechniqueUniversité de Neuchâtel

Prof. P. Thomann (Directeur du LTF)Dr. G. Mileti (Directeur adjoint du LTF)Dr. C. AffolderbachDr. C. SchoriDr. E. BreschiF. FüzesiP. Scherler

Open positions: 2 postdocs, 2 pHDs

Research activities

Primary Cs fountains (METAS)

Laser cooling

Rubidium clocks

Coherent Population Trapping

Chip scale atomic clocks

Stabilised laser diodes

Optical frequency standards


Tower clocks (1300)verge-and-foliot mechanism

Precision / Stabilityin seconds

per day

1 ns

1 µs

100 ps

10 s

1000 s

Huygens Pendulum (1650)pendulum

Marine chronometers

(1750), Harrison

1 ms

Atomic clocks

(1950)

Hydrogen

Maser,

Caesium beam,

Rubidium clock

Quartz oscillators

(1930)

1 s

Earth rotation

10 ns

10 ps

The metamorphosis oftime measurement

-3000 -1500 -170 800 1300 1600 19001700 2000

Marine chronometers Space atomic clocks


Overview

1. A few fundamentals on atomic clocks

2. Examples of atomic clock principles

3. Accuracy and stability of atomic clocks

4. New atomic clocks: exploiting laser pumping

and laser cooling

5. Trends for the (near) future


Essential Bibliography

• Jacques Vanier, Claude Audoin, “The Quantum

Physics of Atomic Frequency Standards”,

Bristol: Adam Hilger, 1989.

• Claude Audoin, Bernard Guinot, Stephen Lyle, “The

Measurement of Time: Time, Frequency and the

Atomic Clock ”, Cambridge, (Original version in

french : Masson, 1998).

• Special issue of Metrologia: “Special issue: fifty

years of atomic time-keeping: 1955 to 2005”,

Volume 42, Number 3, June 2005.


1. Fundamentals on atomic clocks

1. Basic principle of an atomic clock

2. Nuclear magnetic resonance

3. The Bloch vector

4. Advantages of atomic clocks

5. Block diagram of an atomic clock


1.1 Basic principle of an atomic clock

Interrogation

Reference for the user (5 MHz)

Feed-back

Quartz oscillator Atoms

Definition in SI system

The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of

the ground state of cesium 133 (1967)

F=4

6 S½

F=3

Hzh

EEFrequency 7706311929120 =

−=ν


1.2 Nuclear magnetic resonance (classical)

• Magnetic moment interacting with

a magnetic field

• Static :

⇒ Larmor precession

• +rotating magnetic field

⇒ magnetic resonance

)()()( tBtmtmdtd

rrr×⋅= γ

Br

mr

oBr

00 B⋅= γω

0ωω =

)(1 tBr

oBr

oBr

sr

)(1 tBr

π pulse

π/2 pulse


1.3 The Bloch vector (Quantum)

Atom (or ensemble of atoms)

Interacting field (RF, microwave, optical)

Bloch vector (fictitious spin)

tie ω2E

1E

∝

spopulationofdifferencequadratureindipoleatomic

phaseindipoleatomic

wvu

h12 EE −

≈ω

• The state of an atom (2 levels) may be represented with

a vector (“Bloch vector”, or “Fictitious spin”) and

its behavior when interacting with a resonant field as a

magnetic moment in a magnetic field.

• Microwave transitions, optical transitions, π/2 pulses, etc.

sr


Examples oBr

2E

1E

=

=

100

wvu

srAtoms in

fundamental state(no field) sr

oBr

2E

1E

=

=

−100

wvu

srAtoms after π

excitation(and field switched off) sr

oBr

2E

1E

Atoms after π / 2excitation

(and field switched off)⇒ quantum

superposition of states

=

=

0)sin()cos(

0

0

tt

wvu

s ωωr

sr


Magnetic resonance allows spin flip.

It is a frequency selective phenomenon

In an atomic clock you exploit this phenomenon to frequency stabilise a quartz oscillator

In each type of clock it is realised on different species, in various configurations and with different detection techniques

Sign

al

Probing frequency

Linewidth


1.4 Advantages of atomic clock (over quartz)

• All (isolated) atoms of the same element and isotope have an

identical structure (energy levels);

• These atoms provide a stable and accurate reference to frequency

stabilize an oscillator;

• It is a fundamental and intrinsic property;

• Less sensitive to environmental effects (temperature, vibrations, etc.)

• Less aging, drift, warm-up time and retrace effect.

But:

• These atoms still interact with their environment (in and out of the

clock) which is responsible of the differences and drifts between the

standards;

• These atoms usually move: Doppler effect, collisions, etc.


Simplified behavior of quartz oscillators


1.5 Block diagram of an atomic clock


2. Examples of atomic clock principles

1. Categories and applications of atomic clocks

2. Alkali atoms in “microwave” clocks

3. Principle of thermal Cesium beams

4. Principle of Rubidium vapor cell standard

5. Other principles of atomic clocks


2.1 Categories and applications of atomic clocks (or frequency standards)

• Primary (Cs) - Secondary

• Passive – Active (H-Maser)

• Commercial (Rb, Cs, H) – Laboratory – “In development”

• Microwave - Optical


Applications of atomic clocks

4 Radioastronomy, Geodesy

(VLBI, Radioastron, etc.)

4 Scientific Research, Instrumentation

(Microgravity, ACES, HYPER, etc.)

4 Navigation & Positioning

(Galileo, GPS, GLONASS, etc.)

4 Telecommunications

(Networks synchronisation, etc.)

4 Metrology, Time scales

(Primary and secondary standards, H-Masers)


2.2 Alkali atoms in “microwave” clocks

• Hydrogen-like atoms: 1 unpaired electron

• Hyperfine structure: interaction of

• Simplified structure:

• Ground state:

nucleousewith µµ rr

S1/2

P1/2

P3/2

lumière(1014 Hz)

micro-onde(109 -1010 Hz)

=

=

000

wvu

sr


133Cs87Rb

5S1/2

F=1

F=2mF = 0mF = -1mF= -2

mF = 1mF = 2

mF = 0mF = -1

mF = 1

6.8346 GHz5S1/2

F=2

F=3

3.0357 GHz

mF = 0mF = -1mF= -2

mF = 1mF = 2mF = 3

mF = -3

mF = 0mF = -1mF= -2

mF = 1mF = 2

6S1/2

F=3

F=4

mF = 0mF = -1mF= -2

mF = 1mF = 2mF = 3

mF = -3

mF = 0mF = -1mF= -2

mF = 1mF = 2mF = 3

mF = -3

9.1926 GHz

mF = 4

mF = -4

87Rb

85Rb

133Cs


2.3 Principle of thermal Cs beams Stern-Gerlach (State selection) and Ramsey interrogation

0)cos()sin(

0

0

tt

ωω

=

000

sr

−100

010

−100


Destruction of fringes contrast due to atomic velocity

distribution


2.4 Principle of Rb cell standards

Optical pumping, Double resonance , Collisions, Light-shift

Lampe Rb87 filtre Rb85 cellule Rb87

S

P

Thermal equilibrium

S

P

Complete optical pumping

S

P

Partial optical pumping


Absorption spectrum of natural rubidiumD2 line (780 nm)with 30 mb of nitrogen

Rb 85 - F=2

Rb 87 - F=2

Rb 85 - F=3

Rb 87 - F=1

Optical frequency detuning [GHz]0 2 4 6 8


excitation d’une lampe 87Rb avec un oscillateur RF (~120 MHz)

filtrage isotopique par une cellule 85Rb

+


Optical pumping, Double resonance, Light-shift, Collisions

cavité micro-onde

détecteur

Lampe Rb87

filtre Rb85

cellule de résonance Rb87

S

P

Double resonance

light

µ-wave5.304x106 5.306x106 5.308x106 5.310x106 5.312x106

0.108

0.112

0.116

0.120

0.124

0.128

Tra

nsm

itted

ligh

t [V

on

10kΩ

]

6.84 GHz - Synthesiser frequency [Hz]



2.5 Other principles of atomic clocks (or frequency standards)

• Hydrogen Masers

• Ion traps

• Optical standards

(molecules, etc.)

see talk of R. Holzwarth


3. Accuracy and stability of atomic clocks

1. Accuracy and stability

2. Primary frequency standards

3. Short-term frequency stability

4. Drift, aging and environmental effects

5. The role of the quartz oscillator and the LO


3.1 Accuracy and stability


3.2 Primary frequency standards


Figure: de P. Gill, «ESA Harmonisation mapping meeting», October 6 2005


3.3 Short-term frequency stability

5.304x106 5.306x106 5.308x106 5.310x106 5.312x1060.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

Tran

smitt

ed li

ght [

V on

10k

Ω]

6.84 GHz - Synthesiser frequency [Hz]

0

0

ωω

∆=Q

21

).(2.0 −

= τσNSQ

Iy

J.Vanier, L.Bernier, IEEE Trans. on Instr. and Meas., Vol. IM-30, No 4, Dec. 1981

Note: linewidth is not everything


10-16

10-15

10-14

10-13

10-12

10-11

10-10

1 10 100 1000 104 105 106 107

Cs beam, magneticCs-beam, laser H-maser, activeH-maser, passiveRb cell, lampRb or Cs cell, laser CS cold

Time interval (s)

Alla

n de

v.


3.4 Drift, aging and environmental effects

buffer-gas mixture:

40 45 50 55 60 65

-1100

-1080

-1060

-1040

-1020

-1000

39 µW 11 µW "no" light

reso

nanc

e sh

ift (H

z)

Cell temperature (°C)

7400

7450

7500

7550

7600

30 µW 11 µW "no" light

reso

nanc

e sh

ift (H

z)

pure N2

pure Ar

45 50 55 60 653252

3253

3254

3255

3256

3257

3258

reso

nanc

e sh

ift (H

z)

Cell temperature (°C)

pure N2: 1.6·10-9 /K

gas mix: < 6·10-11 /K

long-term stability:temperature within few mK

clock stability around 10-14


3.5 The role of the quartz oscillator and LO

Microwave frequency

LO (quartz)

- Direct AM noise and FM → AM noise

- Aliasing effects (Phase noise)

“Dick effect”

Tran

smitt

ed li

ght

See Deng et al., PRA 59 (1) 773 (1999)

( ) ( ) 2/1

1

22 2 −

∞

=− ⋅= ∑ ττσ φ

nmnnoisePMy nfSC See Mileti et al.,

IEEE J. of Q. Electr. 34 (2) 233 (1998)

Finally:

( ) ( ) ( ) ( )2222 )()()()( τστστστσ lsy

noisePMy

noiseIy

totaly ++≈


4. New atomic clocks: exploiting laser pumping and laser cooling

1. Tunable diode lasers

2. Optically-pumped thermal Cesium beam

3. Laser-pumped vapour cell standard

4. Coherent Population Trapping (CPT)

5. Cold atoms clocks

6. Other standards using diode lasers


4.1 Tuneable diode lasers

Potential advantages of using diode lasers:

• More efficient atomic state preparation / selection:

Examples: optical pumping in Rb, Cs, Maser

• Improved detection of atomic states (S/N):

Examples: optical pumping in Rb, Cs, Maser

• Possibility to slow (cool) or trap atoms

Examples: cold atoms frequency standards

• Explore new physical phenomena

Examples: Coherent Population Trapping

• Miniaturization, etc.

Open issues: availability, reliability, cost, etc.


1.50um

Examples of Laser diodes

Solitary Fabry-Perot (FP)

Extended cavity lasers (ECDL)

Distributed Bragg Reflectors (DBR)

Distributed Feedback (DFB)

FP with DBR optical fiber

Vertical Cavity Surface Emitting (VCSEL)

MEMS based ECDL and VCSEL

Etc.

FP (RWL)

ECDL

DFB

DBR

5 cm

VCSEL


Laser spectral cacterisationExam

ple

1:

het

erodyn

e fr

equen

cy s

pec

trum

Exam

ple

2:

mode-

hope

free

tunin

g r

ange

Laboratory ECDL vsLaboratory ECDL

ESA-ECDL vs DBR ESA-ECDL vs DFB

Laboratory ECDL DBR DFB

133.2 133.6 134.0 134.4-39

-38

-37

-36

-35

-34

-33

550 kHz

dBm

Fourrier frequency [MHz]

129 130 131 132 133 134 135 136 137 138 139-66

-65

-64

-63

-62

5 MHz

dBm

Fourrier frequency [MHz]132 133 134 135 136 137 138

-38

-36

-34

-32

-30

-28

2 MHz

29.05.2003 15:27:57

Am

plitu

de [d

Bm

]

Fourrier frequency [MHz]

>> 15 GHz

Abs

orpt

ion

Wavelength

8 GHz

wavelength

Mode hop

Rb 87 Rb 85

4 GHz

Phot

ocur

rent

Wavelength


100 101 102 103 104 105

10-13

10-12

10-11

10-10

10-9

Spec Rb clock Doppler sub-Doppler

Sampling time τ (s)

Alla

n de

viat

ion

of th

e la

ser f

requ

ency

σy(τ

)

-50 0 50 100 150 200 250

-0.1

0.0

0.1

0.2

sign

al d

'erre

ur U

err (

V)

fréquence laser (MHz)

Laser frequency stabilisation


4.2 Optically-pumped thermal Cs beam


4.3 Laser-pumped vapour cell standardcavité micro-onde

Lampe Rb87 filtre Rb85

6.8 GHz

Rb87 Discharge lamp(several lines, > 1 GHz wide)

Laser (1 line, < 100 MHz wide)

3 GHz

Rb85 Optical filter

détecteur

cellule de résonance Rb87

Potential advantages:

• More efficient pumping

• Improved S/N

• Long term stability

• Power / Weight / Volume

• Redundancy


Laser-pumped Rb prototypeESA-funded project

Volume for control electronics(300cm3,currently empty)

• adapted resonance cell,

• lamp removed,

(empty volume!)

Physics package(200cm3)

RAFS resonator module:

Stabilised laser head:


-4 -2 0 2 4 6 80

5

10

15

20

25

30

D2 lines of Rb87

F = 1F = 2

Phot

ocur

rent

[mA]

Laser diode frequency [GHz]

-4 -2 0 2 4 6 80

50

100

150

200

250

300

350

400

450

Maximal slope : 600 Hz / GHz

Maximal slope : 420 Hz / GHz

Rubi

dium

clo

ck fr

eque

ncy

[Hz]

Laser diode frequency [GHz]-1000 -800 -600 -400 -200 0 200 400 600 800

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

10-8

Referen

ce ab

sorpt

ion lin

e

"10

MH

z" C

lock

freq

uenc

y (-

9'99

9'99

6) [H

z]

Laser frequency detuning [MHz]

-200 -180 -160 -140 -120 -100 -80 -60 -40 -20 0 200.64

0.68

0.72

0.76

0.80

0.84

0.88

"zer

o lig

ht-s

hift"

lase

r fre

quen

cy

Rb8

7 C

O 2

1-23

Rb8

7 C

O 2

2-23

2·10-9

Reference saturated absorption

"10

MH

z" c

lock

freq

uenc

y (-

9'99

9'99

6) [H

z]

Laser frequency detuning [MHz]

Light-shiftShift of the resonance frequency induced by the optical radiation (I, ν)


4.4 Coherent Population Trapping (CPT)

S

P

Coherent Population Trapping“dark” state

Potential advantages of using CPT:

• No microwave cavity

• Reduced light-shift

Open issues: 2-colours coherent laser source, signal contrast


4.5 Cold atoms clocks

)](cos[),( 0 rtEêtrE L φω +⋅⋅=Radiative forces:

4444 34444 21444 3444 21

forcepressureradiationoredissipativ

stab

forcedipolarorreactive

stab rrEvdêrEudêF )()()( 00 φ∇⋅⋅⋅⋅+∇⋅⋅⋅=

~ light-shift ~ absorption

Optical trapping (lattice, tweezers, etc.) Optical molasses

Motivations: reduce the Doppler effect, increase interaction time, etc.


Sisyphus cooling: a combination of effects


Application to cold atoms clocks:

Thermal beam: v = 100 m/s, T = 5 ms∆ν = 100 Hz

Fountain: v = 4 m/s, T = 0.5 s∆ν = 1 Hz

Cold beam in micro-gravity: v = 0.05 m/s, T = 5 s∆ν = 0.1 Hz


Pulsed fountain

-100 -50 0 50 1000.0

0.2

0.4

0.6

0.8

1.0

-1.0 -0.5 0.0 0.5 1.00.0

0.2

0.4

0.6

0.8

1.0

Frequency(Hz)

0.94 Hz



Continuous fountain

0.3

0.2

0.1

0.0

Tran

sitio

n pr

obab

ility

/ a. u

.

-1000 0 1000fRF - fCs / Hz

0.3

0.2

0.1

-15 -10 -5 0 5 10 15

mF = 0

Main motivations:

reduce the effects of LO phase noise (stability) and

collisions (accuracy)


5. Trends for the (near) future

(Optical frequency standards: see next talk)

• Chip-scale atomic clocks

Stable reference

See Knappe et al., Appl. Phys. Lett., 85, (9), 2004


RbRb

alignment and bonding

-0.03 -0.02 -0.01 0.00 0.01 0.02 0.03

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

Abs

orpt

ion

[arb

.]

Frequency [arb.]

87Rb

85Rb


Physics & micro-technology in chip scale atomic clocks:

• Micro-fabrication of the atomic resonator

• Behavior of the confined atoms: collisions, wall-coating, etc.

• Ideal clock scheme: double resonance, Coherent Population Trapping, etc.

• Miniature optical source: control of the optical spectrum and its effects

• Miniature microwave sources: PM noise

• Overall clock electronics: consumption, etc.

• Assembly and packaging, reliability, wafer-scale production, etc.

Physics of Atomic clocks - sps.ch · G. Mileti, Engelberg, 6.3.2007 Laboratoire Temps - Fréquence-5-Essential Bibliography • Jacques Vanier, Claude Audoin, “The Quantum Physics

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