Stability of a Vortex in a Rotating Trapped Bose-Einstein Condensate*

Elizaveta Markovna Artemova, Alexander Alexandrovich Kilin

The problem of stability of rotating regular vortex N-gons (Thomson's configurations) in a Bose–Einstein condensate in a harmonic trap is considered. A reduction procedure on the level set of the momentum integral is proposed. The dependence of the velocity of rotation ω of vortex polygon about the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration, R. The analysis of the orbital linear and nonlinear stability of the motion of such configurations is carried out. For N ⩽ 6, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for N>6 are unstable for any parameters of the system. In this paper, we study the stability of rotating regular vortex N-gons in a Bose–Einstein condensate in a harmonic trap. The analysis of the orbital linear and nonlinear stability of motion is carried out. The dependence of the stability of regular vortex N-gons on the number of vortices N and the parameters of the system is given.

G. M. Kavoulakis

Ramavarmaraja Kishor Kumar, Thangarasu Sriraman, Henrique Fabrelli +2 more

Abstract We study three-dimensional vortex lattice structures in purely dipolar Bose–Einstein condensate (BEC). By using the mean-field approximation, we obtain a stability diagram for the vortex states in purely dipolar BECs as a function of harmonic trap aspect ratio ( λ ) and dipole–dipole interaction strength ( D ) under rotation. Rotating the condensate within the unstable region leads to collapse while in the stable region furnishes stable vortex lattices of dipolar BECs. We analyse stable vortex lattice structures by solving the three-dimensional time-dependent Gross–Pitaevskii equation in imaginary time. Further, the stability of vortex states is examined by evolution in real-time. We also investigate the distribution of vortices in a fully anisotropic trap by increasing eccentricity of the external trapping potential. We observe the breaking up of the condensate in two parts with an equal number of vortices on each when the trap is sufficiently weak, and the rotation frequency is high.

Alexander L. Fetter

Ian R. Coddington, P. C. Haljan, Peter Engels +1 more

Alexander Alexandrovich Kilin, Elizaveta Markovna Artemova

We consider the problem of the stability of rotating regular vortex N-gons (Thomson configurations) in a Bose-Einstein condensate in a harmonic trap. The dependence of the rotation velocity ω of the Thomson configuration around the center of the trap is obtained as a function of the number of vortices N and the radius of the configuration R. The analysis of the stability of motion of such configurations in the linear approximation is carried out. For N⩽6, regions of orbital stability of configurations in the parameter space are constructed. It is shown that vortex N-gons for N > 6 are unstable for any parameters of the system.