On stability of vortices in three-dimensional self-attractive Bose-Einstein condensates

Results of accurate analysis of stability are reported for localized vortices in the Bose-Einstein condensate (BEC) with the negative scattering length, trapped in an anisotropic potential with the aspect ratio root Omega. The cases of Omega >> 1 and Omega << 1 correspond to the "pancake" (nearly-2D) and "cigar-shaped" (nearly-1D) configurations, respectively (in the latter limit, the vortices become "tubular" solitons). The analysis is based on the 3D Gross-Pitaevskii equation. The family of solutions with vorticity S = 1 is accurately predicted by the variational approximation. The relative size of the stability area for the vortices with S = 1 (which was studied, in a part, before) increases with the decrease of Omega in terms of the number of atoms, but decreases in terms of the chemical potential. All states with S >= 2 are unstable, while the stability of the ordinary solitons (S = 0) obeys the Vakhitov-Kolokolov criterion. The stability predictions are verified by direct simulations of the full 3D equation. (c) 2006 Elsevier B.V. All rights reserved.