Wave Packet Echo in Optical Lattice and Decoherence Time

Chao ZhuangU(t)

Aug. 15, 2006CQISC2006

University of Toronto

Aephraim Steinberg

Matthew Partlow

Samansa ManeshiJalani Kanem

Department of Physics, Center for Quantum Information and Quantum Control, Institute for Optical SciencesUniversity of Toronto

Outline• Pulse echo

– Two level system– Life time: T1, T2, T2

*

– How it works & in What system• Wave packet echo in optical lattice

– Setup and Measurement– Optimize echo pulse– Decoherence and coherence control

Something General

v

w

u

Ω

T1 longitudinal lifetime De-population

T2 transverse homogeneous lifetime De-coherence

T2* transverse inhomogeneous lifetime De-phase

0

1

0

0 1a b 1

00

1

0

0 10 1

Pulse echo: How it works

10

pulse, 2 2

t

v

w

uρ

0Ω

ρ

ρ

0 δ

ρ

10

after pulse, 2 2

t

0( )ρ

Free Evolution

1t ( )t

( )δ

3 20

pulse, t t

*2 2t T

0( )ρ

3 20

after pulse, t t Free Evolution

4 overlap

revive to max

t

*1 2 2 pulseT T T t

Pulse echo: Timeline

t

t

1t 2t0 4t3t

pulse2

pulse

*2T

P

*2T*

2T

Pulse echo: Why it’s important Inhomogeneous decay due to dephasing

can be reversed!

(De)coherence time due to homogeneous decay can be measured directly.

Coherence time decides how long quantum information can be stored in a quantum system.

Pulse echo: What system Spin Echo

Nuclear Magnetic Resonance E. L. Hahn, Phys. Rev. 80, 580 (1950)

Photon Echo Optical Resonance N. A. Kurnit, I. D. Abella, and S. R. Hartmann,

Phys. Rev. Lett. 13, 567 (1964) Wave Packet Echo

F. B. J. Buchkremer, R. Dumke, H. Levsen, G. Birkl, and W. Ertmer, Phys. Rev. Lett. 85, 3121 (2000)

Optical LatticeOptical lattices are periodic potentials formed by the ac Stark shift (light shift) seen by atoms when they interact with a set of interfering laser beams.

I. H. Deutsch and P. S. Jessen, Phys. Rev. A 57, 1972(1998).

& Wave Packet

Motional atoms in optical lattice

Motional wave packets in optical lattice

Experimental Setup: Vertical Optical Lattice

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

Thermal 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

Measuring State Population

v

w

u

dephasing due to lattice depth inhomogeneities ~ T2*

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

coherence preparation shift

0

t

t

t = 0

measurement shift

θ

Measuring Coherence: Oscillations in the Lattice

Dephasing due to primarily lattice inhomogeneities

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 500 1000 1500 2000 2500

t

Anatomy of an Echo

original oscillation

oscillation from echo pulse

the echo itself

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

2D Fourier Spectroscopy

memory

det

exc

*2

1

T

echo pulse

apply detectexcdet

memory

echo pulse

apply exc detect det

det

exc

Initial Results

driv

e fr

eq. [

Hz]

observed oscillation freq. [Hz]

driven ‘monochromatically’ with 10 cycles

What if we try “bang-bang”?(Repeat pulses before the bath gets amnesia; trade-off since each pulseis imperfect.)

“bang-bang” pulse sequences...Some coherence out to > 3 ms now...

• Optimisation of certain class of echo pulses• Preliminary work on 3D lattice• Preliminary work on characterization of

frequency response of the system due to Quasi-monochromatic excitation

• Observation of higher-order Echoes

Future work• Characterize homogeneous and

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

Summary