Stability of vortices in inhomogeneous Bose condensates subject to rotation: A three-dimensional analysis

We study numerically the stability of axially symmetric vortex lines in trapped dilute gases subject to rotation. For this purpose, we solve numerically both the Gross-Pitaevskii and the Bogoliubov equations for a three-dimensional condensate in spherically and cylindrically symmetric traps, from small to very large nonlinearities. In the stationary case we find that the vortex states with $m=1\mathrm{}$ and $m=2\mathrm{}$ are energetically unstable. In the rotating trap it is found that this energetic instability may only be suppressed for the $m=1\mathrm{}$ vortex line, and that the multicharged vortices are never a local minimum of the energy functional. This result implies that the absolute minimum of the energy is not an eigenstate of the $L_z$ operator, when the angular speed is above a certain value.