Bose-Einstein condensates with vortices in rotating traps

We investigate minimal energy solutions with vortices for an interacting Bo se-Einstein condensate in a rotating trap. The atoms are strongly confined along the axis of rotation z, leading to an effective 2D situation in the x -y plane. We first use a simple numerical algorithm converging to local min ima of energy. Inspired by the numerical results we present a variational a nsatz in the regime where the interaction energy per particle is stronger t han the quantum of vibration in the harmonic trap in the x-y plane, the so- called Thomas-Fermi regime. This ansatz allows an easy calculation of the e nergy of the vortices as function of the rotation frequency of the trap; it gives a physical understanding of the stabilisation of vortices by rotatio n of the trap and of the spatial arrangement of vortex cores. We also prese nt analytical results concerning the possibility of detecting vortices by a time-of-flight measurement or by interference effects. In the final sectio n we give numerical results for a 3D configuration.