Preserving Coherence of Atoms and
Characterizing Decoherence Processes in an
Optical Lattice
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
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
AOM2
PBS
TUI
Amplifier
Grating Stabilized Laser
AOM1

PBS
85Rb
Cold
atoms
T ~ 8μK
Lattice spacing ~ 0.93μm
Spatial filter
Function
Generator
PBS
Controlling phase of AOMs
allows control of lattice
position
Measuring State Populations
Thermal state
Initial Lattice
Ground State
1st Excited State
After adiabatic decrease
Well
Depth
Isolated ground state
0
t1
t(ms)
Preparing a ground state
t1+40
2 bound states
1 bound state
7 ms
0
t1
t1+40
Oscillations in the Lattice
displace the lattice
ˆ 0
D
0
coherence preparation shift
a 0  b 1  ...
P0
0.8
θ
0
t=0
0.7
decaying oscillations
0.6
t
0.5
0.4
t
pre-measurement shift
0.3
0.2
P (t )  0 D
1
  U t  D   0
2
200
400
600
800 1000 1200 1400 1600
dephasing due to lattice depth inhomogeneities
t(μs)
Echo in the Lattice
(using lattice shifts and delays as coupling pulses)
θ
0
1
echo (amp. ~ 9%) ; max. 13%
(see also Buchkremer
et. al. PRL 85, 3121(2000))
single shift
t
Losssingle~80%
0.8
θ
0
echo (amp. ~ 16%)
0.6
double shift + delay
tp~ (2/5 T)
t
0.4
0
0.2
Lossdouble~60%
θ
echo (amp. ~ 19%)
rms~ (T/8)
t(s) 1000 1200 1400 1600 1800 2000 2200 2400
Uo =18ER ,T = 190μs, tpulse-center = 900s
Gaussian pulse
t
LossGaussian~45%
Preliminary data on Coherence time in 1D and 3D Lattice
0.08
1D
0.07
echo amplitude
3D
0.06
0.05
0.04
0.03
0.02
0.01
0
2000
2200
2400
2600
2800
echo at (s)
Decoherence due to
• transverse motion of atoms
• inter-well tunneling,
3000
3200
Higher-Order Echoes (Dynamical Decoupling)
P0
1.4
0
400
800
1200
1600
t(s) 0
1.4
200 400 600 800 1000 1200 1400
1.2
1.2
decaying oscillations
1
1
0.8
0.8
0.6
0.4
0.6
expected 2nd order echo
•
•
•
0.4
expected 3rd order echo
•
•
•
0.2
0.2
2000
2400
oscill’ns due to pulse
pulse1
pulse2
2800
3200
1st order echo
21of pulse1
T = 2.2ms
0
t(s) 2500
500μs
3000
1ms
3500
1ms
4000
500μs
T ´= 3ms
2D Fourier Spectroscopy
echo pulse
apply exc
detect det
echo pulse
detect det
apply exc
memory
det
det
memory
exc

1
T2*
exc
Quasi-Monochromatic Excitation
drive with 5-period sinusoid instead of abrupt shift
1.6
1.4
abrupt shift
responds at T=210μs
1.2
1
drive at  = 150μs
responds at T=180μs
0.8
0.6
drive at  = 190μs
responds at T=200μs
0.4
0.2
0
200
400
600
t(s)
800 1000 1200
Preliminary data on Linear Fourier Spectroscopy
Observe Center Frequency(Hz)
7000
Frequency Power Spectrum 0.6
Frequency Spectrum
0.55
6500
0.5
6000
0.45
0.4
5500
0.35
5000
0.3
4500
4000
4000
0.25
4500
5000
5500
6000
6500
Driving Center Frequency (Hz)
7000 4000
4500
5000
5500
6000
6500
Driving Center Frequency(Hz)
width ~1400Hz
0.2
7000
Summary
• 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