Eur. Phys. J. D 22, 235-257 (2003)
https://doi.org/10.1140/epjd/e2003-00015-y

Bose-Einstein condensates with a bent vortex in rotating traps

¹ INFM - LENS - Dipartimento di Fisica, Università di Firenze, Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
² Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, case 121, 4 place Jussieu, 75252 Paris Cedex 05, France
³ Laboratoire Kastler Brossel, École Normale Supérieure, 24 rue Lhomond, 75005 Paris, France

Corresponding author: ^a yvan.castin@lkb.ens.fr

Received: 28 March 2002
Revised: 13 September 2002
Published online: 21 January 2003

Abstract

We consider a 3D dilute Bose-Einstein condensate at thermal equilibrium in a rotating harmonic trap. The condensate wavefunction is a local minimum of the Gross-Pitaevskii energy functional and we determine it numerically with the very efficient conjugate gradient method. For single vortex configurations in a cigar-shaped harmonic trap we find that the vortex line is bent, in agreement with the numerical prediction of Garcia-Ripoll and Perez-Garcia [Phys. Rev. A 63, 041603 (2001)]. We derive a simple energy functional for the vortex line in a cigar-shaped condensate which allows to understand physically why the vortex line bends and to predict analytically the minimal rotation frequency required to stabilize the bent vortex line. This analytical prediction is in excellent agreement with the numerical results. It also allows to find in a simple way a saddle point of the energy, where the vortex line is in a stationary configuration in the rotating frame but not a local minimum of energy. Finally we investigate numerically the effect of thermal fluctuations on the vortex line for a condensate with a straight vortex: we can predict what happens in a single realization of the experiment by a Monte Carlo sampling of an atomic field quasi-distribution function of the density operator of the gas at thermal equilibrium in the Bogoliubov approximation.