Jalani F. Kanem 1, Samansa Maneshi 1, Matthew Partlow 1, Michael Spanner 2 and Aephraim Steinberg 1 Center for Quantum Information & Quantum Control, Institute for Optical Sciences, 1 Department of Physics, 2 Department of Chemistry, University of Toronto Observation of High-order Quantum Resonances in the Kicked Rotor

Outline: Kicked Rotor analogue with optical lattice Quantum resonances Experimental setup Data & simulations 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, (1995) Possible probe of lattice inter-well coherence ? INTRODUCTION

Ideal Delta Kicked Rotor Optical Lattice realization

 g Kicked Rotor T ideallattice implementation Ideal Rotor Atom optics realization

 g Kicked Rotor 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 T ideallattice implementation Scaled quantum Schrödinger’s: 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

Discuss classical vs. quantum behaviour of momentum diffusion? Classically chaotic: momentum diff. ~ N 1/2 Quantum: dynamic localization and/or quantum resonance

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.

TUI PBS AOM1 AOM2 Amplifier Grating Stabilized Laser Function Generator Individual control of frequency and phase of AOMs allows control of lattice velocity and position. Spatial filter Experimental Setup Note: optical standing wave is in vertical direction ‘hot’ un-bound atoms fall out before kicking begins ~3 recoil energies 1m1m Tilted due to gravity  A tilted lattice would affect the dynamics of the experiment, therefore we accelerate the lattice downward at g to cancel this effect.

The System Preparation : ● 85 Rb vapor cell MOT ● 10 8 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) Typical pulse parameters : ●  s pulse period ● 5-15  s pulse length ● Depth of recoil units (~2-12  K) ● chaos parameter  = 1-10 ● scaled Planck's constant =1-10

Raizen reference And Reference paper that figure is from 2π2π 4π4π Past experiments with thermal clouds

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

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

Simulations interesting conclusion ? Describe widths used for simulations

Conclusions have observed high-order quantum resonances in atom-optics implementation of the kicked rotor visibility due to using 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/

EXTRAS

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Windell Oskay/University of Texas at Austin

Energy growth / resonance resolution Quadratic growth ???