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Conference on Lasers and Electro-Optics

Stability properties of vortex states in trapped two-dimensional Bose condensate

Han Pu, C. K. Law, N. P. Bigelow, Joseph H. Eberly

Published Jan 1, 1998• 0 citations
Publisher

Abstract

Summary form only given.The study of the properties of vortices is one of the major subfields of superfluidity. In helium II, it has been shown that a hydrodynamic instability involving vortex lines can be caused by counterflow along the lines, an effect involving the interplay between normal and super-fluids. Here, we present a study on the stability property of the vortex states of a condensate confined in a two-dimensional harmonic spherical potential at zero temperature. Our work does not take the thermal atoms into account, but instead focuses on the intrinsic coupling between vortex states.

DOI
10.1109/iqec.1998.680111

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Summary form only given.The study of the properties of vortices is one of the major subfields of superfluidity. In helium II, it has been shown that a hydrodynamic instability involving vortex lines can be caused by counterflow along the lines, an effect involving the interplay between normal and super-fluids. Here, we present a study on the stability property of the vortex states of a condensate confined in a two-dimensional harmonic spherical potential at zero temperature. Our work does not take the thermal atoms into account, but instead focuses on the intrinsic coupling between vortex states.
We study the ground state properties of a two-dimensional Bose gas in an harmonic trap potential using the recently proposed mean-field equation that takes into account the correct dimensionality effect. In contrast to the three-dimensional case, the interaction term depends logarithmically on the scattering length and density. We compare our results with other approaches with various forms for the two-dimensional coupling. We also consider the vortex states and study the effects of density-dependent interactions on the formation of vortices.
We consider the intrinsic stability of the vortex states of a pure Bose-Einstein condensate confined in a harmonic potential under the effects of a coherent atom-atom interaction. We find that stable vortices can be supported and vortex stability can be controlled by changing the interparticle interaction strength. At unstable regimes, a vortex will spontaneously disintegrate into states with different angular momenta even without external perturbations, with the lifetime determined by its imaginary excitation frequencies.
Vortex states of weakly interacting Bose-Einstein condensates confined in three-dimensional rotating harmonic traps are investigated numerically at zero temperature. The ground state in the rotating frame is obtained by propagating the Gross-Pitaevskii equation for the condensate in imaginary time. The total energies between states with and without a vortex are compared, yielding critical rotation frequencies that depend on the anisotropy of the trap and the number of atoms. Vortices displaced from the center of nonrotating traps are found to have long lifetimes for sufficiently large numbers of atoms. The relationship between vortex stability and bound core states is explored.
We compute the structure of a quantized vortex line in a harmonically trapped dilute atomic Bose-Einstein condensate using the Popov version of the Hartree-Fock-Bogoliubov mean-field theory. The vortex is shown to be (meta)stable in a nonrotating trap even in the zero-temperature limit, thus confirming that weak particle interactions induce for the condensed gas a fundamental property characterizing "classical" superfluids. We present the structure of the vortex at ultralow temperatures and discuss the crucial effect of the thermal gas component to its energetic stability.
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 trapped single-component Bose–Einstein condensates within self-consistent mean-field theories; in particular, we consider the Hartree–Fock–Bogoliubov–Popov theory and its recently proposed gapless extensions. It is shown that for sufficiently repulsively interacting systems the anomalous negative-energy modes related to vortex instabilities are lifted to positive energies due to partial filling of the vortex core with noncondensed gas. Such behaviour implies that within these theories the vortex states are eventually stable against the transfer of condensate matter to the anomalous core modes. This self-stabilization of vortices, shown to occur under very general circumstances, is contrasted to the predictions of the non-self-consistent Bogoliubov approximation, which is known to exhibit anomalous modes for all vortex configurations and thus implying instability of these states. In addition, the shortcomings of these approximations in describing the properties of vortices are analysed, and the need for a self-consistent theory taking properly into account the coupled dynamics of the condensate and the noncondensate atoms is emphasized.