Wave Packet Echo in Optical Lattice and Decoherence Time
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Transcript of Wave Packet Echo in Optical Lattice and Decoherence Time
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Wave Packet Echo in Optical Lattice and Decoherence Time
Chao ZhuangU(t)
Aug. 15, 2006CQISC2006
University of Toronto
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Aephraim Steinberg
Matthew Partlow
Samansa ManeshiJalani Kanem
Department of Physics, Center for Quantum Information and Quantum Control, Institute for Optical SciencesUniversity of Toronto
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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
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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
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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
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Pulse echo: Timeline
t
t
1t 2t0 4t3t
pulse2
pulse
*2T
P
*2T*
2T
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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.
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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)
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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
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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
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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
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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
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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
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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%
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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
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2D Fourier Spectroscopy
memory
det
exc
*2
1
T
echo pulse
apply detectexcdet
memory
echo pulse
apply exc detect det
det
exc
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Initial Results
driv
e fr
eq. [
Hz]
observed oscillation freq. [Hz]
driven ‘monochromatically’ with 10 cycles
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What if we try “bang-bang”?(Repeat pulses before the bath gets amnesia; trade-off since each pulseis imperfect.)
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“bang-bang” pulse sequences...Some coherence out to > 3 ms now...
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• 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