Three-dimensional vortex configurations in a rotating Bose Einstein condensate

We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross Pitaevskii equation. Following recent experiments [Rosenbuch et al, Phys. Rev. Lett., 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the x-z or y-z plane. S type vortices exist for all values of the angular velocity Omega while U vortices exist for Omega sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices.