Three-dimensional vortex configurations in a rotating Bose Einstein condensate

We consider a rotating Bose-Einstein condensate in a harmonic trap and investigate numerically the behavior of the wave function which solves the Gross Pitaevskii equation. Following recent experiments [Rosenbuch et al, Phys. Rev. Lett., 89, 200403 (2002)], we study in detail the line of a single quantized vortex, which has a U or S shape. We find that a single vortex can lie only in the x-z or y-z plane. S type vortices exist for all values of the angular velocity Omega while U vortices exist for Omega sufficiently large. We compute the energy of the various configurations with several vortices and study the three-dimensional structure of vortices

Low-lying excitations of a trapped rotating Bose-Einstein condensate

We investigate the low-lying excitations of a weakly-interacting, harmonically-trapped Bose-Einstein condensed gas under rotation, in the limit where the angular mometum $L$ of the system is much less than the number of the atoms $N$ in the trap. We show that in the asymptotic limit $N \to \infty$ the excitation energy, measured from the energy of the lowest state, is given by $27 N_{3}(N_{3}-1) v_0 /68$, where $N_{3}$ is the number of octupole excitations and $v_{0}$ is the unit of the interaction energy.Comment: 3 pages, RevTex, 2 ps figures, submitted to PR

Anomalous rotational properties of Bose-Einstein condensates in asymmetric traps

We study the rotational properties of a Bose-Einstein condensate confined in a rotating harmonic trap for different trap anisotropies. Using simple arguments, we derive expressions for the velocity field of the quantum fluid for condensates with or without vortices. While the condensed gas describes open spiraling trajectories, on the frame of reference of the rotating trap the motion of the fluid is against the trap rotation. We also find explicit formulae for the angular momentum and a linear and Thomas-Fermi solutions for the state without vortices. In these two limits we also find an analytic relation between the shape of the cloud and the rotation speed. The predictions are supported by numerical simulations of the mean field Gross-Pitaevskii model.Comment: 4 RevTeX pages, 2 EPS figures; typos fixed, reference adde

Globally-Linked Vortex Clusters in Trapped Wave Fields

We put forward the existence of a rich variety of fully stationary vortex structures, termed H-clusters, made of an increasing number of vortices nested in paraxial wave fields confined by trapping potentials. However, we show that the constituent vortices are globally linked, rather than products of independent vortices. Also, they always feature a monopolar global wave front and exist in nonlinear systems, such as Bose-Einstein condensates. Clusters with multipolar global wave fronts are non-stationary or at best flipping.Comment: 4 pages, 5 PostScript figure