Vortices in a trapped dilute Bose-Einstein condensate.

摘要

We discuss the structure, energy, dynamics, normal modes and stability of a vortex line in large Bose-Einstein condensates. Using the method of matched asymptotic expansions, we derive a general nonlinear equation governing the vortex motion and investigate normal modes of the vortex for 2D and 3D condensates. We take into account the nonuniform nature of the system (trap potential), the vortex curvature and a possible trap rotation. For an axisymmetric trap, all normal mode frequencies are real and the motion of the vortex line is a superposition of plane-polarized standing-wave modes. In 2D condensates, the planar modes are degenerate, and their superposition can result in helical traveling waves, which differs from 3D condensates.; In a nonuniform condensate the excitation spectrum of the vortex includes anomalous mode(s) with negative frequency. Trap rotation shifts the normal-mode frequencies and can stabilize the vortex line. For a cigar-shape condensate, the vortex curvature makes a significant contribution to the frequency of the lowest unstable mode; furthermore, additional modes with negative frequencies appear. As a result, it is considerably more difficult to stabilize a central vortex in a cigar-shape condensate than in a disc-shape one. Apart from the vortex modes, we investigate the condensate modes and show that the vortex line splits the degenerate normal modes of an axisymmetric condensate by a small amount of order of the ratio of the vortex core size and the condensate dimension. Results of our theory are in a good quantitative agreement with recent experiments on vortex dynamics performed in Boulder, USA, and in Paris, France.; We consider also the effect of thermal quasiparticles on vortex normal modes and demonstrate that they can stabilize the vortex line.