Observation of High-order Quantum Resonances in the Kicked Rotor

1. Observation of High-order Quantum Resonances in the Kicked Rotor Jalani F. Kanem1, Samansa Maneshi1,MatthewPartlow1, Michael Spanner2 andAephraim Steinberg1 Center for Quantum Information & Quantum Control, Institute for Optical Sciences, 1Department of Physics, 2Department of Chemistry, University of Toronto

2. INTRODUCTION • The quantum kicked rotor is a rich system for studying quantum-classical correspondence, decoherence, and quantum dynamics in general • Atom optics systems provide excellent analogue: • Atom Optics Realization of the Quantum Delta-Kicked Rotor • Raizen group - PRL 75, 4598-4601 (1995) • • Possible probe of lattice inter-well coherence ? • Outline: • Kicked Rotor analogue with optical lattice • Quantum resonances • Experimental setup • Data & simulations

3. Ideal Delta Kicked Rotor Optical Lattice realization

4. g  T Kicked Rotor ideal lattice implementation Ideal Rotor Atom optics realization

5. g  T Scaled Planck's constant is a measure of how 'quantum' the system is. The smaller , the greater the quantum classical correspondence ~ ratio of quantized momentum transfer from lattice to momentum required to move one lattice spacing in one kick period, T Kicked Rotor ideal lattice implementation Scaled quantum Schrödinger’s: Stochasticity parameter: system becomes chaotic when strength or period of kicks are large enough that atoms (rotor) travel more than one lattice spacing (2 between kicks.→Force on atom is a random variable

6. Discuss classical vs. quantum behaviour of momentum diffusion? Classically chaotic: momentum diff. ~ N1/2 Quantum: dynamic localization and/or quantum resonance

7. Quantum Resonances • Resonances → dramatically increased energy absorption • Due to rephasing of momentum states coupled by the lattice potential whose momentum differ by a multiple of : • 2π, 4π, etc. ‘easy’ to observe: all momentum states rephase e.g. wavepacket revival • High-order resonance, s>1, fractional revival, only some quasimomentum states rephase.

8. AOM2 PBS TUI Amplifier Grating Stabilized Laser AOM1  PBS PBS Spatial filter Individual control of frequency and phase of AOMs allows control of lattice velocity and position. Function Generator 1m Tilted due to gravity ~3 recoil energies Experimental Setup Note: optical standing wave is in vertical direction ‘hot’ un-bound atoms fall out before kicking begins A tilted lattice would affect the dynamics of the experiment, therefore we accelerate the lattice downward at g to cancel this effect.

9. Typical pulse parameters: • 50-150s pulse period • 5-15s pulse length • Depth of 30-180 recoil units (~2-12K) • chaos parameter  = 1-10 • scaled Planck's constant =1-10 The System Preparation: • 85Rb vapor cell MOT • 108 atoms • Cooled to ~10K • Load a 1-D optical lattice supporting 1-2 bound states (~14 recoil energies) • Initial rms velocity width of ~5mm/s (255nK)

10. Past experiments with thermal clouds Raizen reference And Reference paper that figure is from 4π 2π

11. Our observed resonances Inset: calculation of resonance-independent quantum diffusion (How much to explain? Make extra slide?)

12. /π = 0.47±0.01, 0.72±0.01, 1, 1.25±0.02, 1.54±0.02 Quantum, not classical: resonance position insensitive to kick strength

13. Simulations Describe widths used for simulations interesting conclusion ?

14. Conclusions have observed high-order quantum resonances in atom-optics implementation of the kicked rotor visibility due tousing lattice to select out cold atoms possibly greater coherence across lattice than we expect? give credit to other observation in the future, control and measurement of quasimomentum This work: arXiv:quant-ph/0604110

15. EXTRAS

16. a

17. Windell Oskay/University of Texas at Austin

19. Energy growth / resonance resolution Quadratic growth ???