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arXiv:cond-mat/9902092 · Physical Review Letters

Coherent Dynamics of Vortex Formation in Trapped Bose-Einstein Condensates

B. M. Caradoc-Davies, R. J. Ballagh, Keith R. Burnett

Published Aug 2, 1999• 119 citations
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Abstract

Simulations of a rotationally stirred condensate show that a regime of simple behavior occurs in which a single vortex cycles in and out of the condensate. We present a simple quantitative model of this behavior, which accurately describes the full vortex dynamics, including a critical angular speed of stirring for vortex formation. A method for experimentally preparing a condensate in a central vortex state is suggested.

DOI
10.1103/physrevlett.83.895

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arXiv:cond-mat/0011104•Journal of Experimental and Theoretical Physics Letters•Dec 1, 2000•0 citations
Simulations of a rotationally stirred condensate show that a regime of simple behavior occurs in which a single vortex cycles in and out of the condensate. We present a simple quantitative model of this behavior, which accurately describes the full vortex dynamics, including a critical angular speed of stirring for vortex formation. A method for experimentally preparing a condensate in a central vortex state is suggested.
We simulate in the mean-field limit the effects of rotationally stirring a three-dimensional trapped Bose-Einstein condensate with a Gaussian laser beam. A single vortex cycling regime is found for a range of trap geometries, and is well described as coherent cycling between the ground and the first excited vortex states. The critical angular speed of stirring for vortex formation is quantitatively predicted by a simple model. We report preliminary results for the collisions of vortex lines, in which sections may be exchanged.
We consider a Bose-Einstein condensate subject to a rotating harmonic potential, in connection with recent experiments leading to the formation of vortices. We use the classical hydrodynamic approximation to the nonlinear Schrödinger equation to determine almost analytically the evolution of the condensate. We predict that this evolution can exhibit dynamical instabilities, for the stirring procedure previously demonstrated at ENS and for a new stirring procedure that we put forward. These instabilities take place within the range of stirring frequency and amplitude for which vortices are produced experimentally. They provide therefore an initiating mechanism for vortex nucleation.
The problem of explaining the critical angular velocity Ω c when the formation of a vortex in the stirred Bose-Einstein condensate becomes energetically possible is considered in the framework of the variational approach. The origin of smallness of the calculated Ω c in comparison with the measured values, which takes place for a pure quantum state with the unit angular momentum per condensed particle, is uncovered. The agreement with the measured Ω c is achieved upon admitting a small admixture of the zero angular-momentum state in the wave function of the one-vortex quantum state prepared after stirring. A portion of this admixture amounts to 1–13% of the total condensed atoms. A possible test of this hypothesis is proposed.