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arXiv:0709.0405 · Physical Review A

Metastability of persistent currents in trapped gases of atoms

K. Kärkkäinen, J. Christensson, Gilbert Reinisch, G. M. Kavoulakis, S. M. Reimann

Published Oct 26, 2007• 11 citations
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Abstract

We examine the conditions that give rise to metastable, persistent currents in a trapped Bose-Einstein condensate. A necessary condition for the stability of persistent currents is that the trapping potential is not a monotonically increasing function of the distance from the trap center. Persistent currents also require that the interatomic interactions are sufficiently strong and repulsive. Finally, any off-center vortex state is shown to be unstable, while a driven gas shows hysteresis.

DOI
10.1103/physreva.76.043627

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We examine the conditions that give rise to metastable, persistent currents in a trapped Bose-Einstein condensate. A necessary condition for the stability of persistent currents is that the trapping potential is not a monotonically increasing function of the distance from the trap center. Persistent currents also require that the interatomic interactions are sufficiently strong and repulsive. Finally, any off-center vortex state is shown to be unstable, while a driven gas shows hysteresis.
We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current.
A quantized vortex in Bose-Einstein condensation (BEC) of an alkali-metal atom gas is known to be unstable intrinsically at zero temperature. We examine two stabilization mechanisms of a vortex theoretically. (i) The finite temperature effect is shown to stabilize a vortex. (ii) An additional pinning potential, which may be produced by a focused laser beam at the vortex center, is also shown to stabilize it even at zero temperature. The mean-field calculation for BEC confined by a harmonic potential is employed. The detailed properties of a stable vortex are given, such as the spatial profiles of the condensate and noncondensate, the particle current density around the core, the whole excitation spectrum, and their temperature dependence.
We study the stability of vortices in a binary system of Bose-Einstein condensat es, with their wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify miscible and immiscible regimes characterized by the inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of Bose-Einstein condensates placed in a rotating harmonic trap and study the single united vortex state in this system. We derive an approximate form for the energy of a single united vortex in the binary system and the critical angular velocity for the global stability of a vortex at the center of the trap. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Numerical solutions to the Gross-Pitaevskii equations support these expressions. These rotational results inform us of a novel bimodal formation within the miscible regime of the binary condensate system. We thus demonstrate the nontrivial aspects of vortex stability in interacting binary Bose-Einstein condensates as a result of their nonlinear interactions.