Vortex stability in nearly-two-dimensional Bose-Einstein condensates with attraction

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 $S=1$ are stable in a third of their existence region, 0 0.43Nₘₐₓ(S=1), 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 √10, the stability interval of the $S=1$ vortices occupies ≈40% 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 $2$. All vortices with S2 are unstable.