Nonlinear Matter Wave Dynamics with a Chaotic Potential

Details Nonlinear Matter Wave Dynamics with a Chaotic Potential Nonlinear Matter Wave Dynamics with a Chaotic Potential

1999-12-20

arxiv.org/abs/quant-ph/9912092v1

Phys. Rev. A 62, 023612 (2000).

Physics

Quantum Physics

20 pages text, 20 gzipped ps and eps figures

Scientific paper

10.1103/PhysRevA.62.023612

We consider the case of a cubic nonlinear Schr\"{o}dinger 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 Schr\"{o}dinger 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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