Vortices in a rotating Bose-Einstein condensate: Critical angular velocities and energy diagrams in the Thomas-Fermi regime - art. no. 063603

For a Bose-Einstein condensate placed in a rotating trap and strongly confi ned along the z axis, we set a framework of study for the Gross-Pitaevskii energy in the Thomas-Fermi regime for an effective two-dimensional (2D) sit uation in the x-y plane. We investigate an asymptotic expansion of the ener gy, the critical angular velocities of nucleation of vortices with respect to a small parameter epsilon, and the location of vortices. The limit epsil on going to zero corresponds to the Thomas-Fermi regime. The nondimensional ized energy is similar to the Ginzburg-Landau energy for superconductors in the high-kappa high-field limit and our estimates rely on techniques devel oped for this latter problem. We also take advantage of this similarity to develop a numerical algorithm for computing the Bose-Einstein vortices. Num erical results and energy diagrams are presented.