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 [P. Rosenbuch, V. Bretin, and J. Dalibard, 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.