Abstract
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional (“pancake-shaped”) trapped Bose-Einstein condensate with negative scattering length. The analysis combines computation of the stability eigenvalues and direct simulations. The states with vorticity are stable in a third of their existence region, , where is the number of atoms, and is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, , the unstable vortex periodically splits in twofragments and recombines. At , the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full three-dimensional (3D) Gross-Pitaevskii equation. In a moderately anisotropic 3D configuration, with the aspect ratio , the stability interval of the vortices occupies of their existence region, hence the two-dimensional (2D) limit provides for a reasonable approximation in this case. For the isotropic 3D configuration, the stability interval expands to 65% of the existence domain. Overall, the vorticity heightens the actual collapse threshold by a factor of up to . All vortices with are unstable.
1 More- Received 28 July 2005
DOI:https://doi.org/10.1103/PhysRevA.73.043615
©2006 American Physical Society