2006/03/29 by Dumitru Mihalache, Dumitru Mazilu, Boris A. Malomed +1 · 1 citation
Physics and Astronomy · #cond-mat.other #nlin.PS
paper · pdf · doi:10.1103/physreva.73.043615
21 pages, 8 figures, to appear in Physical Review A
arxiv created 2006/03/29 · arxiv updated 2009/12/01
We perform accurate investigation of stability of localized vortices in an effectively two-dimensional ("pancake-shaped") trapped BEC 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<N<(1/3)Nmax(S=1), where N is the number of atoms, and Nmax(S=1) is the corresponding collapse threshold. Stable vortices easily self-trap from arbitrary initial configurations with embedded vorticity. In an adjacent interval, (1/3)Nmax (S=1)<N< \allowbreak 0.43Nmax(S=1), the unstable vortex periodically splits in two fragments and recombines. At N> \allowbreak 0.43Nmax(S=1), the fragments do not recombine, as each one collapses by itself. The results are compared with those in the full 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 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 S≥ 2 are unstable.