Nonlinear matter wave dynamics with a chaotic potential - art. no. 023612

We consider the case of a cubic nonlinear Schrodinger equation with an addi tional chaotic potential, in the sense that such a potential produces chaot ic dynamics in classical mechanics. We derive and describe an appropriate s emiclassical limit to such a nonlinear Schrodinger equation, using a semicl assical interpretation of the Wigner function, and relate this to the hydro dynamic limit of the Gross-Pitaevskii equation used in the context of Bose- Einstein condensation. We investigate a specific example of a Gross-Pitaevs kii equation with such a chaotic potential, the one-dimensional delta-kicke d harmonic oscillator, and its semiclassical limit, discovering in the proc ess an interesting interference effect, where increasing the strength of th e repulsive nonlinearity promotes localization of the wave function. We exp lore the feasibility of an experimental realization of such a system in a B ose-Einstein condensate experiment, giving a concrete proposal of how to im plement such a configuration, and considering the problem of condensate dep letion.