Bose-Einstein condensates with vortices in rotating traps |
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Authors: | Y Castin R Dum |
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Institution: | (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, FR;(2) Institut d'Optique, Université Paris-Sud, batiment 503, B.P. 147, 91403 Orsay Cedex, France, FR |
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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 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.
Received 16 December 1998 and Received in final form 18 March 1999 |
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Keywords: | PACS 03 75 Fi Phase coherent atomic ensembles quantum condensation phenomena - 67 40 Vs Vortices and turbulence - 32 80 Pj Optical cooling of atoms trapping |
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