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Journal of Optics B Quantum and Semiclassical Optics

Momentum distributions for the quantum δ-kicked rotor with decoherence

Andrew C. Doherty, Kendra vant, G. Ball, Nelson L Christensen, R. Leonhardt

Published Oct 1, 2000• 20 citations
Publisher

Abstract

We discuss the theoretical description and numerical simulation of the effect of noise and environmental coupling on the momentum distribution of the quantum δ-kicked rotor in recent atom optics experiments. We investigate the transition between exponentially localized and more nearly Gaussian momentum distributions and compare our simulations with existing experimental results.

DOI
10.1088/1464-4266/2/5/307

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We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.
We study analytically the effect of amplitude noise on the quantum resonances of an atom optics realization of the δ-kicked rotor. Noise is shown to add a time growth to the ‘deterministic’ energy and to induce a time increasing spreading in the momentum distribution; exact results are given for both effects. The ballistic peaks characteristic of the noiseless distribution for particular initial conditions broaden and eventually vanish, whereas the associated quadratic growth of energy persists; at large times, the survival probability decays as t −1 . Moreover, the nonexponential ‘localization’ linked to different initial conditions is gradually destroyed. Features specific to Gaussian noise, white and coloured, are analysed. The feasibility of experimental tests of these effects is discussed.
We experimentally investigate the effects of phase noise on the resonant and non-resonant dynamics of the atom-optics kicked rotor. Employing sinusoidal phase modulation at various frequencies, resonances are found corresponding to periodic phase shifts, resulting in the effective transformation of quantum anti-resonances into resonances and vice-versa. The stability of the resonance is analysed, with the aid of experiments, -classical theory and numerical simulations, and is found to be surprisingly robust against phase noise. Finally we look into the effects of phase noise on dynamical localization and discuss the destruction of the localization in terms of decoherence.
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