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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