THREE-DIMENSIONAL SIMULATIONS OF QUANTIZED VORTICES IN ROTATING BOSE-EINSTEIN CONDENSATES

Quantized vortices were first predicted and discovered in superfluid. The first experimental realization in 1995 of a Bose-Einstein condensate (BEC) has opened novel research directions on the properties associated to vortices in a macroscopic system with quantum properties. The reason is that a dilute-gas BEC is a highly controllable system which supports a simple theoretical description. Different methods are experimentally used to generate vortices in a BEC: moving an object (laser beam) through the condensates, rotating the condensate, and, recently, imprinting topological defects by phase-engineering. He4 In this paper, we review our recent numerical results on the vortex structure of rotating BECs. This work was motivated by recent experimental achievements by the École Normale Supérieure (ENS) group. Using real experimental parameters in a three-dimensional (3D) numerical simulation of fast rotating BECs is a challenging proposition since the capture of the large number of vortices in the system requires high grid-resolution and accurate numerical methods. Our numerical results are obtained by propagating the three-dimensional Gross-Pitaevskii equation in imaginary time. A high order (compact) finite difference method is used for the spatial discretization. We characterize several equilibrium vortex configurations obtained for different trapping potentials. Numerical data are compared to available experimental and theoretical results and a remarkably good qualitative and quantitative agreement is found