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arXiv · 0711.0153

Matter-wave vortices in cigar-shaped and toroidal waveguides

Luca Salasnich·Flavio Toigo·Boris A. Malomed
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Abstract

We study vortical states in a Bose-Einstein condensate (BEC) filling a cigar-shaped trap. An effective one-dimensional (1D) nonpolynomial Schroedinger equation (NPSE) is derived in this setting, for the models with both repulsive and attractive inter-atomic interactions. Analytical formulas for the density profiles are obtained from the NPSE in the case of self-repulsion within the Thomas-Fermi approximation, and in the case of the self-attraction as exact solutions (bright solitons). A crucially important ingredient of the analysis is the comparison of these predictions with direct numerical solutions for the vortex states in the underlying 3D Gross-Pitaevskii equation (GPE). The comparison demonstrates that the NPSE provides for a very accurate approximation, in all the cases, including the prediction of the stability of the bright solitons and collapse threshold for them. In addition to the straight cigar-shaped trap, we also consider a torus-shaped configuration. In that case, we find a threshold for the transition from the axially uniform state, with the transverse intrinsic vorticity, to a symmetry-breaking pattern, due to the instability in the self-attractive BEC filling the circular trap.

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Luca Salasnich, Flavio Toigo, Boris A. Malomed. 2007-11-01. Matter-wave vortices in cigar-shaped and toroidal waveguides. https://doi.org/10.1103/physreva.76.063614

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