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arXiv:cond-mat/0503673

Microscopic Theory of Trapped Two-Dimensional Bose Gas

Kalai Kumar Rajagopal

Published Mar 29, 2005• 0 citations
arXivHTMLPDF

Abstract

This report is based on my incomplete Phd thesis. The final part of the work on the 2D Yukawa bosons/vortices in a confined geometry is not complete and subject to futher development.
DOI
10.48550/arxiv.cond-mat/0503673

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The connection between quantized vortices and dark solitons in a waveguidelike trap geometry is explored in the framework of the nonlinear Schr\"odinger equation. Variation of the transverse confinement leads from the quasi-one-dimensional (1D) regime, where solitons are stable, to 2D (or 3D) confinement, where soliton stripes are subject to a transverse modulational instability known as the ``snake instability.'' We present numerical evidence of a regime of intermediate confinement where solitons decay into single, deformed vortices with solitonic properties rather than vortex pairs as associated with the ``snake'' metaphor. Further relaxing the transverse confinement leads to the production of two and then three vortices, which correlates perfectly with a Bogoliubov stability analysis. The decay of a stationary dark soliton (or, planar node) into a single solitonic vortex is predicted to be experimentally observable in a 3D harmonically confined dilute-gas Bose-Einstein condensate.