Professor Simon Gardiner s.a.gardiner@durham.ac.uk
Professor
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 δ-kicked harmonic oscillator, and its semiclassical limit, discovering in the process an interesting interference effect, where increasing the strength of the repulsive nonlinearity promotes localization of the wave function. We explore the feasibility of an 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.
Gardiner, S., Jaksch, D., Dum, R., Cirac, J., & Zoller, P. (2000). Nonlinear matter wave dynamics with a chaotic potential. Physical Review A, 62(2), https://doi.org/10.1103/physreva.62.023612
Journal Article Type | Article |
---|---|
Publication Date | 2000-08 |
Journal | Physical review. A. |
Print ISSN | 1050-2947 |
Publisher | American Physical Society |
Peer Reviewed | Peer Reviewed |
Volume | 62 |
Issue | 2 |
DOI | https://doi.org/10.1103/physreva.62.023612 |
Publisher URL | http://link.aps.org/abstract/PRA/v62/e023612 |
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Book Chapter
Selected theoretical comparisons for bosons.
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Bright solitary matter waves: formation, stability and interactions.
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Introduction to theoretical modelling
(2013)
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Number-conserving approaches for atomic Bose-Einstein condensates: an overview.
(2013)
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