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Physical Review Letters

Quantum Enhancement of Momentum Diffusion in the Delta-Kicked Rotor

M. B. d’Arcy, R. M. Godun, Markus K Oberthaler, Donatella Cassettari, G. S. Summy

Published Jul 30, 2001• 144 citations
Publisher

Abstract

We present detailed observations of the quantum delta-kicked rotor in the vicinity of a quantum resonance. Our experiment consists of an ensemble of cold cesium atoms subject to a pulsed off-resonant standing wave of light. We measure the mean energy and show clearly that at the quantum resonance it is a local maximum. We also examine the effect of noise on the system and find that the greatest sensitivity to this occurs at the resonances. This makes these regions ideal for examining quantum-classical correspondence. A picture based on diffraction is developed which allows the experiments to be readily understood.

DOI
10.1103/physrevlett.87.074102

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We present detailed observations of the quantum delta-kicked rotor in the vicinity of a quantum resonance. Our experiment consists of an ensemble of cold cesium atoms subject to a pulsed off-resonant standing wave of light. We measure the mean energy and show clearly that at the quantum resonance it is a local maximum. We also examine the effect of noise on the system and find that the greatest sensitivity to this occurs at the resonances. This makes these regions ideal for examining quantum-classical correspondence. A picture based on diffraction is developed which allows the experiments to be readily understood.
We report on the experimental observation of environment induced decoherence in the quantum delta-kicked rotor. Ultracold cesium atoms are subjected to a pulsed standing wave of near resonant light. Spontaneous scattering of photons destroys dynamical localization thereby giving rise to a quantum diffusion, which approaches the classical diffusion with an increasing degree of decoherence. This tendency is enhanced by a stronger stochasticity in the underlying classical system. A comparison with theoretical predictions is presented.
We measure the momentum of cold cesium atoms in a periodically pulsed standing wave of light. This system is an experimental realization of the quantum kicked rotor. The momentum diffusion in the (chaotic) classical analog of this system is typically suppressed by quantum localization. We find, however, that for certain pulse amplitudes where the classical system exhibits anomalous diffusion, our momentum distributions are not exponentially localized. We observe a predicted correspondence between the classical and quantum energy growth as a function of pulse amplitude and period.
We describe measurements of the mean energy of an ensemble of laser-cooled atoms in an atom optical system in which the cold atoms, falling freely under gravity, receive approximate delta-kicks from a pulsed standing wave of laser light. We call this system a "delta-kicked accelerator." Additionally, we can counteract the effect of gravity by appropriate shifting of the position of the standing wave, which restores the dynamics of the standard delta-kicked rotor. The presence of gravity (delta-kicked accelerator) yields quantum phenomena, quantum accelerator modes, which are markedly different from those in the case for which gravity is absent (delta-kicked rotor). Quantum accelerator modes result in a much higher rate of increase in the mean energy of the system than is found in its classical analog. When gravity is counteracted, the system exhibits the suppression of the momentum diffusion characteristic of dynamical localization. The effect of noise is examined and a comparison is made with simulations of both quantum-mechanical and classical versions of the system. We find that the introduction of noise results in the restoration of several signatures of classical behavior, although significant quantum features remain.
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 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.