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arXiv:cond-mat/0101014 · Physical Review A

Vortices in Bose-Einstein condensates confined in a multiply connected Laguerre-Gaussian optical trap

Jacques Tempere, J. T. Devreese, E. R. I. Abraham

Published Jul 5, 2001• 39 citations
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Abstract

The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterion for vortex stability is that the interatomic interaction strength must exceed a critical interaction strength. The time evolution of a freely expanding Laguerre-Gaussian condensate with a vortex is calculated and used to derive the interference pattern of such a condensate overlapping with a parabolically trapped condensate.

DOI
10.1103/physreva.64.023603

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The quantized vortex state is investigated in a Bose-Einstein condensate, confined in a multiply connected geometry formed by a Laguerre-Gaussian optical trap. Solving the Gross-Pitaevskii equation variationally, we show that the criterion for vortex stability is that the interatomic interaction strength must exceed a critical interaction strength. The time evolution of a freely expanding Laguerre-Gaussian condensate with a vortex is calculated and used to derive the interference pattern of such a condensate overlapping with a parabolically trapped condensate.
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We investigate the existence and especially the linear stability of single- and multiple-charge quantized vortex states of nonlinear Schr\"odinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by an examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confinement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triple-charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher-charge vortices are more unstable for both types of potentials, and their dynamical evolution leads to a breakup into single-charged vortices.
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.
The quantized vortex states of a weakly interacting Bose-Einstein condensate of atoms with attractive interatomic interaction in an axially symmetric harmonic oscillator trap are investigated using the numerical solution of the time-dependent Gross-Pitaevskii equation obtained by the semi-implicit Crank-Nicholson method. The collapse of the condensate is studied in the presence of deformed traps with the larger frequency along either the radial or the axial direction. The critical number of atoms for collapse is calculated as a function of the vortex quantum number L. The critical number increases with increasing angular momentum L of the vortex state but tends to saturate for large L.
The expansion of Bose-Einstein condensates with quantized vortices is studied by solving numerically the time-dependent Gross-Pitaevskii equation at zero temperature. For a condensate initially trapped in a spherical harmonic potential, we confirm previous results obtained by means of variational methods showing that, after releasing the trap, the vortex core expands faster than the radius of the atomic cloud. This could make the detection of vortices feasible, by observing the depletion of the density along the axis of rotation. We find that this effect is significantly enhanced in the case of anisotropic disk-shaped traps. The results obtained as a function of the anisotropy of the initial configuration are compared with the analytic solution for a noninteracting gas in three dimensions as well as with the scaling law predicted for an interacting gas in two dimensions.
Multiquantum vortices in dilute atomic Bose-Einstein condensates confined in long cigar-shaped traps are known to be both energetically and dynamically unstable. They tend to split into single-quantum vortices even in the ultralow temperature limit with vanishingly weak dissipation, which has also been confirmed in the recent experiments [Y. Shin et al., Phys. Rev. Lett. 93, 160406 (2004)] utilizing the so-called topological phase engineering method to create multiquantum vortices. We study the stability properties of multiquantum vortices in different trap geometries by solving the Bogoliubov excitation spectra for such states. We find that there are regions in the trap asymmetry and condensate interaction strength plane in which the splitting instability of multiquantum vortices is suppressed, and hence they are dynamically stable. For example, the doubly quantized vortex can be made dynamically stable even in spherical traps within a wide range of interaction strength values. We expect that this suppression of vortex-splitting instability can be experimentally verified.