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arXiv:quant-ph/0604110 · Physical Review Letters

Observation of High-Order Quantum Resonances in the Kicked Rotor

J. F. Kanem, Samansa Maneshi, Matthew J. Partlow, M. Spanner, Aephraim M. Steinberg

Published Feb 23, 2007• 64 citations
arXivHTMLPDF

Abstract

Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.

DOI
10.1103/physrevlett.98.083004

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Quantum resonances in the kicked rotor are characterized by a dramatically increased energy absorption rate, in stark contrast to the momentum localization generally observed. These resonances occur when the scaled Planck's constant Planck's [over ]=r/s 4pi, for any integers r and s. However, only the variant Planck's [over ]=r2pi resonances are easily observable. We have observed high-order quantum resonances (s>2) utilizing a sample of low energy, noncondensed atoms and a pulsed optical standing wave. Resonances are observed for variant Planck's [over ]=r/16 4pi for integers r=2-6. Quantum numerical simulations suggest that our observation of high-order resonances indicate a larger coherence length (i.e., coherence between different wells) than expected from an initially thermal atomic sample.
We have observed high-order quantum resonances in a realization of the quantum delta-kicked rotor, using Bose-condensed Na atoms subjected to a pulsed standing wave of laser light. These resonances occur for pulse intervals that are rational fractions of the Talbot time, and are characterized by ballistic momentum transfer to the atoms. The condensate's narrow momentum distribution not only permits the observation of the quantum resonances at 3/4 and 1/3 of the Talbot time, but also allows us to study scaling laws for the resonance width in quasimomentum and pulse interval.
We report the first direct experimental realization of the quantum $\ensuremath{\delta}$-kicked rotor. Our system consists of a dilute sample of ultracold sodium atoms in a periodic standing wave of near-resonant light that is pulsed on periodically in time to approximate a series of delta functions. Momentum spread of the atoms increases diffusively with every pulse until the "quantum break time" after which exponentially localized distributions are observed. Quantum resonances are found for specific values of the pulse period.
We present experimental observations of diffusion resonances for the quantum kicked rotor with weak decoherence. Cold caesium atoms are subject to a pulsed standing wave of near-resonant light, with spontaneous emission providing environmental coupling. The mean energy as a function of the pulse period is determined during the late-time diffusion period for a constant probability of spontaneous emission. Structure in the late-time energy is seen to increase with physical kicking strength. The observed structure is related to Shepelyansky's predictions of the initial quantum diffusion rates. Additional results of diffusion rates as a function of the effective Planck's constant are given, showing non-trivial behaviour in the quantum-to-classical transition regime.
We investigate analytically and numerically early-time momentum diffusion rates for the delta-kicked rotor across the quantum to classical transition, i.e., as increased total system action produces more macroscopic dynamics. For sufficiently narrow initial momentum distributions we find a rich structure of resonances in these diffusion rates as a function of the effective Planck's constant. Our study is set in the physical context of the atom optics kicked rotor, and numerical simulations confirm that the resonances persist with kicks of finite duration and with other typical experimental imperfections, such as spontaneous emission noise. Our results should be testable in experiments where narrow initial momentum distributions are prepared using, for example, velocity selective Raman transitions or Bose-Einstein condensates.
In this thesis we investigate quantum resonant effects in the atom-optical ὁ-kicked accelerator. Using Floquet analysis, we theoretically study the time evolution of quantum systems which have a classical counterpart that exhibits chaotic dynamics. We introduce quantum resonance and quantum antiresonance features of the quantum ὁ -kicked rotor by setting the pulse period to an integer multiple of the half-Talbot time. The model is generalised to the atom-optical ὁ -kicked accelerator by considering thermal alkali atoms subject to a periodically pulsed standing wave potential formed from counter-propagating laser beams. The dynamics of the momentum distribution is analysed by evaluating the momentum moments and momentum cumulants. We derive analytic solutions for these observables for the ultracold and thermal limiting cases, and observe fractional quantum resonant phenomena. Simulations have been developed to examine the time evolution for individual momentum eigenstates, which we use to construct a non-interacting finite temperature gas, based upon a Monte Carlo method. We investigate the temperature dependence of the ὁ-kicked rotor, neglecting gravitational effects, and show that the atomic dynamics is highly sensitive to the initial momentum width of the gas. A generalisation of the model to quantify the transition between the ultracold and thermal temperature regimes of the atom-optical ὁ -kicked accelerator is examined using linear regression analysis. High order quantum resonance features are found to be sensitive to the relative acceleration between the atomic gas and the pulsed optical standing wave. We assess the dependence of the ὁ -kicked accelerator upon gravitational acceleration, quantifying the width of the high order quantum resonance features, which we use to assess the prospect for precision measurement using a finite temperature gas.