Stationary arrays of vortices in Bose–Einstein condensates confined by a toroidal trap

Abstract

We numerically study metastable arrays of vortices in three-dimensional Bose–Einstein condensates by solving the Gross–Pitaevskii equation with initial imprinted vorticity. We consider condensates confined by a harmonic plus Gaussian potential such as that used in a recent experiment. We analyse the energy barrier that prevents the vortices from leaving the trap and the spatial distribution of vortices for different trap parameters and winding numbers. For configurations forming rings of vortices we interpret the results in terms of the velocity fields produced by the vortices themselves and the spatial inhomogeneity of the condensate. For low enough densities, we found stationary configurations of multiply quantized vortices.