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Observation of High-order Quantum Resonances in the Kicked Rotor Jalani F. Kanem1, Samansa Maneshi1, Matthew Partlow1, Michael Spanner2 and Aephraim Steinberg1 Center for Quantum Information & Quantum Control, Institute for Optical Sciences, 1Department of Physics, 2Department of Chemistry, University of Toronto 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 Ideal Delta Kicked Rotor Optical Lattice realization Kicked Rotor ideal g lattice implementation T Ideal Rotor Atom optics realization Kicked Rotor ideal g lattice implementation T 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 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. ~ N1/2 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. • Experimental Setup AOM2 PBS TUI Amplifier Grating Stabilized Laser AOM1 PBS Note: optical standing wave is in vertical direction ‘hot’ un-bound atoms fall out before kicking begins Spatial filter Function Generator 1m ~3 recoil energies Tilted due to gravity PBS Individual control of frequency and phase of AOMs allows control of lattice velocity and position. 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: ● 85Rb ● 108 atoms ● Cooled to ~10K vapor cell MOT Load a 1-D optical lattice supporting 1-2 bound states (~14 recoil energies) Typical pulse parameters: ● 50-150s pulse period ● 5-15s pulse length Depth of 30-180 recoil units (~2-12K) ● ● Initial rms velocity width of ~5mm/s (255nK) ● ● chaos parameter = 1-10 ● scaled Planck's constant =1-10 Past experiments with thermal clouds Raizen reference And Reference paper that figure is from 2π 4π 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 Describe widths used for simulations interesting conclusion ? 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/0604110 EXTRAS a Windell Oskay/University of Texas at Austin Energy growth / resonance resolution Quadratic growth ???