Eur. Phys. J. D 7, 399-412 (1999)
https://doi.org/10.1007/s100530050584

Bose-Einstein condensates with vortices in rotating traps

¹ Laboratoire Kastler Brossel (Unité de recherche de l'École Normale Supérieure et de l'Université Pierre et Marie Curie, associée au CNRS.) , École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France
² Institut d'Optique, Université Paris-Sud, bâtiment 503, B.P. 147, 91403 Orsay Cedex, France

Received: 16 December 1998
Revised: 18 March 1999
Published online: 15 October 1999

Abstract

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 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 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.