1. Chao Zhuang, Samansa Maneshi, XiaoXian Liu, Ardavan Darabi, Chris Paul, Luciano Cruz, and Aephraim Steinberg Department of Physics, Center for Quantum Information and Quantum Control, Institute for Optical Sciences University of Toronto Coherent Control of Vibrational States in a Tilted-Washboard Potential

2. Motivation  Optical lattices are a leading candidate system for quantum information processing  Lattices are also an important arena for studying condensed-matter and many-body phenomena  We are working to understand decoherence in these systems (see also talk KJF787 by S. Maneshi)  Here, we study how well the quantum states of atoms in lattices may be controlled, using quantum coherence Outline Experimental setup State population measurement Square pulse (example of coherent control) Phase Modulation (PM) Amplitude Modulation (AM) Coherent control by AM plus PM Conclusions

3. Vertical 1D Optical Lattice - Experimental Setup MOT: Cold 85 Rb atoms T ~ 10μK  =10 10 atoms/cm 3 Optical Lattice: Lattice spacing : a ~ 0.93μm Effective lattice recoil energy (E R )~ 32nK U 0 =(18-20)E R = (580-640)nK  =10 5 atoms/plane

4. Measuring State Populations

5. Coupling by Square Pulse (Example of Coherent Control) Phys. Rev. A 77, 022303 (2008) Samansa Maneshi, et al. T = 160  s ; U 0 ~ 30 E R Simulation P0P0 P1P1 P Loss Experimental Data

6. Coupling by Square Pulse (Example of Coherent Control)

7. Coupling by Phase Modulation (PM) Period of the pulse T = 190μs U 0 ~ 20 E R P 0 = 0.461 P 1 = 0.313 P2 = 0.221 We have good coupling between the ground and 1 st excited state, but big losses too. P0P0 P Loss P1P1

8. Coherent Control of Atomic Vibration Sinusoidal modulation of the intensity of both lattice beam AM Sinusoidal modulation of the phase of one lattice beam PM Interference between these two kinds of pulses provides a method to minimize losses

9. AM + PM Simulation a pm = 5 o f pm = 5kHz ; cycle number = 4 a am = 10% I 0 f am = 10kHz ; cycle number = 8 P0P0 P Loss P1P1

10. AM + PM Preliminary Data a pm = 6 o f pm = 5kHz ; cycle number = 4 a am = 36% I 0 f am = 10kHz ; cycle number = 8 P0P0 P1P1 P Loss

11. Conclusions We showed the feasibility of coherent control in tilted optical lattices by square pulse coupling We demonstrated the efficiency of phase modulation (PM) in the coupling of vibrational states. The aplication of AM and PM together provide a method to control losses. This method yields the possibility to process quantum information in the optical lattice for long times efficiently. Future work Optimal control of vibrational quantum states GRAPE (GRadient Ascent Pulse Engineering) Algorithm Genetic Algorithm