Samansa Maneshi, Jalani Kanem, Chao Zhuang, Matthew Partlow Aephraim Steinberg Department of Physics, Center for Quantum Information and Quantum Control,

Samansa Maneshi, Jalani Kanem, Chao Zhuang, Matthew Partlow

Aephraim Steinberg

Department of Physics, Center for Quantum Information

and Quantum Control, Institute for Optical Sciences

University of Toronto

Preserving Coherence of Atoms and Characterizing Decoherence Processes in an Optical Lattice

Motivation

Controlling coherence of quantum states is the fundamental problem in

the field of quantum information processing

Need to characterize real world systems and be able to perform error

corrections with no a priori knowledge of the errors

Outline

Measuring quantum states in the lattice

Coherence in the lattice and Pulse-echo

2D spectroscopy and characterization of broadening

Vertical Optical Lattice Experimental Setup

Cold 85Rb atoms T ~ 8μKLattice spacing ~ 0.93μm

Controlling phase of AOMs allows control of lattice position

Function Generator

AOM1

TUIPBS

AOM2

Amplifier

PBS PBSSpatial filter

Grating Stabilized Laser

Measuring State PopulationsThermal state

Ground State

1st Excited State

Initial Lattice

After adiabatic decrease

Well Depth

t(ms)0 t1 t1+40

Isolated ground state

Preparing a ground state

t1+40

2 bound states

0 t1

7 ms

1 bound state

Oscillations in the Lattice

displace the lattice

0 ˆ 0D 0 1 ...a b

dephasing due to lattice depth inhomogeneities

y = m3*sin(m0*2*3.14/m1+m2)*...

ErrorValue

1.1254208.54m1

0.0271141.801m2

0.00726640.33918m3

0.00150330.46156m4

5.6669238.96m5

NA0.43667Chisq

NA0.9413R

200 400 600 800 1000 1200 1400 1600

t(μs)

P0

decaying oscillations

0.2

0.3

0.4

0.5

0.6

0.7

0.8

2

1( ) 0 0P t D U t D

coherence preparation shift

0

t

t

t = 0

pre-measurement shift

θ

Echo in the Lattice(using lattice shifts and delays as coupling pulses)

echo (amp. ~ 19%)

echo (amp. ~ 16%)

echo (amp. ~ 9%)

double shift + delay

0

tp~ (2/5 T)

θ

t

rms~ (T/8)

θ

Gaussian pulse

0

t

tLosssingle~80%

Lossdouble~60%

LossGaussian~45%

0

single shift

θ

Uo =18ER ,T = 190μs, tpulse-center = 900s

0.2

0.4

0.6

0.8

1

1000 1200 1400 1600 1800 2000 2200 2400t(s)

(see also Buchkremer et. al. PRL 85, 3121(2000))

; max. 13%

Preliminary data on Coherence time in 1D and 3D Lattice

Decoherence due to • transverse motion of atoms

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

2000 2200 2400 2600 2800 3000 3200

1De

cho

am

pli

tud

e

echo at (s)

• inter-well tunneling,

3D

Higher-Order Echoes (Dynamical Decoupling)P0

• ••

expected 2nd order echo

2000 2400 2800 3200

0 400 800 1200 1600

0.2

0.4

0.6

0.8

1

1.2

1.4

1st order echo 21of pulse1

oscill’ns due to pulse

pulse1 pulse2T = 2.2ms

0

0.2

0.4

0.6

0.8

1

1.2

1.4

2500 3000 3500 4000

0 200 400 600 800 1000 1200 1400

t(s)

t(s)

• ••

expected 3rd order echo

T ´= 3ms

500μs 500μs1ms 1ms

decaying oscillations

2D Fourier Spectroscopy

memory

det

exc

*2

1

T

echo pulse

apply detectexcdet

memory

echo pulse

apply exc detect det

det

exc

Quasi-Monochromatic Excitation

drive with 5-period sinusoid instead of abrupt shift

abrupt shift responds at T=210μs

drive at = 150μsresponds at T=180μs

drive at = 190μsresponds at T=200μs

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 200 400 600 800 1000 1200

t(s)

Frequency Power Spectrum

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0.6

4000 4500 5000 5500 6000 6500 7000

Driving Center Frequency(Hz)

Preliminary data on Linear Fourier Spectroscopy

width ~1400Hz

4000

4500

5000

5500

6000

6500

7000

4000 4500 5000 5500 6000 6500 7000

Ob

se

rve

Ce

nte

r F

req

ue

nc

y(H

z)

Driving Center Frequency (Hz)

Frequency Spectrum

• Optimisation of certain class of echo pulses: • Larger echo amplitude and less loss of atoms due to Gaussian pulse compared to square and simple pulse

• Observation of higher-order Echoes• Preliminary work on characterization of frequency

response of the system due to Quasi-monochromatic excitation

Future work • Characterize homogeneous and inhomogeneous broadening through 2D FT spectroscopy • Design adiabatic pulses for inversion of states • Study decoherence due to tunneling

Summary