We investigate minimal energy solutions with vortices for an interacting
Bose-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 minima of
energy. Inspired by the numerical results we present a variational Ansatz in
the regime where the interaction energy per particle is stronger than 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 energy of
the vortices as function of the rotation frequency of the trap; it gives a
physical understanding of the stabilisation of vortices by rotation of the trap
and of the spatial arrangement of vortex cores. We also present analytical
results concerning the possibility of detecting vortices by a time-of-flight
measurement or by interference effects. In the final section we give numerical
results for a 3D configuration.Comment: 15 pages, 16 figures, to be published in Eur. Phys. Jour. D; one
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