Nonlinear Matter Wave Dynamics with a Chaotic Potential
Abstract
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.
Cite
@article{arxiv.quant-ph/9912092,
title = {Nonlinear Matter Wave Dynamics with a Chaotic Potential},
author = {S. A. Gardiner and D. Jaksch and R. Dum and J. I. Cirac and P. Zoller},
journal= {arXiv preprint arXiv:quant-ph/9912092},
year = {2009}
}
Comments
20 pages text, 20 gzipped ps and eps figures