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Nonlinear Matter Wave Dynamics with a Chaotic Potential

S. A. Gardiner·D. Jaksch·R. Dum·J. I. Cirac·P. Zoller
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Abstract

We consider the case of a cubic nonlinear Schrödinger equation with an additional chaotic potential, in the sense that such a potential produces chaotic dynamics in classical mechanics. We derive and describe an appropriate semiclassical limit to such a nonlinear Schrödinger equation, using a semiclassical interpretation of the Wigner function, and relate this to the hydrodynamic limit of the Gross-Pitaevskii equation used in the context of Bose-Einstein condensation. We investigate a specific example of a Gross-Pitaevskii equation with such a chaotic potential: the one-dimensional delta-kicked harmonic oscillator, and its semiclassical limit. We explore the feasibility of experimental realization of such a system in a Bose-Einstein condensate experiment, giving a concrete proposal of how to implement such a configuration, and considering the problem of condensate depletion.

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S. A. Gardiner, D. Jaksch, R. Dum, J. I. Cirac, P. Zoller. 1999-12-20. Nonlinear Matter Wave Dynamics with a Chaotic Potential. https://doi.org/10.1103/physreva.62.023612

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