Vortices in rotating trapped dilute Bose-Einstein condensates

The basic physics of a dilute trapped Bose gas reflects both the interparticle interactions and the quantum degeneracy. At low temperatures, nearly all the particles are in the condensate. The corresponding macroscopic wave function obeys the time-dependent Gross-Pitaevskii equation that describes the dynamical evolution (formally equivalent to a nonlinear Schrodinger equation). The dynamics of a single vortex in a rotating condensate can be studied in various different ways. (i) One method examines how the energy changes as the vortex is displaced from the central position and predicts the onset of metastability at a critical angular velocity Omega(m). (ii) A more direct dynamical approach considers the small-amplitude perturbations and finds a negative frequency if the applied angular velocity Omega is smaller than Omega(m) for onset of metastability (this behavior indicates a Landau type of instability for Omega < Omega(m)). Both analyses predict the precession frequency of an off-center vortex line, in good agreement with measured values. For larger external rotation rates, the number of vortices increases and a triangular vortex lattice forms. In the limit of rapid rotations, the centrifugal forces expand the condensate radially and shrink it axially. This altered aspect ratio provides a reliable estimate of the actual rotation rate. (C) 2004 Elsevier B.V. All rights reserved.