1. Cold atoms in Optical lattice, vibrational states, coherent control via interference between one- and two-phonon excitation, and a little bit about decoherence,
Chao Zhuang
Quantum Optics Day 2009
Department of Physics
University of Toronto
Aephraim Steinberg
Luciano Cruz
Samansa Maneshi
Nick Chisholm
Ardavan Darabi
XiaoXian Liu
Chris Paul

2. Outline Experiment Setup Things I will talk about
Interference between one- and two-phonon excitation
Coherent control using one- and two-phonon
Possible way of probing decoherence
Things I will talk a little about
Echo experiment
Pump-probe experiment

3. Experiment Setup

4. 1D vertical lattice
1D optical lattice: interference of two laser beams g

5. Cold atoms in optical latticeg
Dilute gas
No interaction between atoms
Fluorescence image
Optical Lattice:
Lattice spacing : a ~ 0.93μm
ER ~ 32nK, U0 =(18-20)ER = ( )nK
=103 atoms/plain
Photon scattering rate ~ 60ms to 100ms
MOT:
Cold 85Rb atoms
T ~ 10μK
=1010atoms/cm3

6. Prepare and measure the states
Initial Lattice
After adiabatic decrease
Thermal state
Well
Depth
t(ms) t1
t1+40

7. Prepare and measure the states
Initial Lattice
After adiabatic decrease
t1+40
2 bound states t1
7 ms
1 bound state
Well
Depth
t(ms)
Isolated ground state

8. Prepare and measure the states
Initial Lattice
After adiabatic decrease
t1+40
2 bound states t1
7 ms
1 bound state
Well
Depth
t(ms)
Isolated ground state

9. Operations of lattice
Use AOM to control the relative phase between the two lattice beams equivalent to displace the lattice in the real space
Use AOM to control the intensity of the lattice beam equivalent to change the lattice depth

10. PM and AM Phase modulation (PM) Amplitude modulation (AM)
Relative phase
Amplitude modulation (AM)
Intensity of laser beam

11. Things I will talk about

12. Interference!
No Interference
No interference
Constructive
Destructive

13. One- v.s. two- phonon excitation
Interference between the transition probability of the one-phonon excitation and two-phonon excitation
aPM
aAM

14. Typical Experiment Data!
AM 20% 8cyc
TAM = 100ms
PM 6o 4cyc
TPM = 200ms

15. How to change the PM loss
Experiment Data
Simulation
aPM
aPM

16. Search with different PM loss
Experiment Data
Simulation

17. Coherent control, one v.s. two
Branching Ratio

18. Only relative phase is varied
Experiment Data
Simulation
Red lines indicate different Branching Ratio

19. Decoherence probe?

20. Things I will talk a little about

21. Decoherence Coherence Possible source of decoherence
The ability to interfere
A stable relative phase
Possible source of decoherence
Atoms see different lattice depths
Atoms move in transverse plain
Tunneling from one well to another
Photon scattering

22. Echo experiment
Atoms see different lattice depths, but each atom sees only one lattice depth
relative phase between ground and excited states
Decoherence: dephasing
Reverse the ground state and excited state at time T, rephase at 2T,
by probing at different 2T, decoherence due to other sources can be observed
Each runner has a different constant running speed

23. Higher-order echo Each runner with a constant acceleration
Atoms are moving, which means the lattice depth each atom sees is changing
N-th order echo can fix (N-1)-th time depend frequency drift
2nd order echo: T-reverse-2T-reverse-T-revive
3rd order echo:
T-reverse-(1+√2)T-reverse
- (1+√2)T-reverse-T-revive

24. Pump-probe experiment
2D contour plot

25. Generic way to predict echo decay
2ms Delay
5ms Delay 0 1 2 N t
...

26. Thank you!
One more comment: Interference is EVERYWHERE and USEFUL!