Coherent Vortex Dynamics in Two- and Three-Dimensional Bose-Einstein Condensates

Abstract

Vortices have been a major interest in Bose-condensed systems since the early studies of super.uid He II. These topological objects in the quantum field have a 2π phase circulation about a point of zero amplitude, and thus allow circulating flow in the (otherwise) irrotational quantum fluid. A classic experiment in superfluidity demonstrated that vortices form as the preferred stable state in a rotating cylinder of He II [1], a result explained theoretically in terms of the equilibrium energy properties of vortices [2]. The recently realised gaseous Bose-Einstein condensates (BEC) provide important new opportunities for the study of vortices in quantum fluids, and in particular of vortex dynamics. A priori theoretical calculations can be more readily made for these weakly interacting gases than for strongly interacting quantum liquids such as He II, and the experiments can make direct and detailed dynamical observations. Initial theoretical studies of vortices in BEC concentrated on static properties including stability and excitation spectra [3]-[6]. Recently, however, a number of dynamical studies of vortices have been made using the Gross-Pitaevskii equation (GPE) for the mean field wavefunction ψ(r, t), which is known to be accurate near T = 0. Jackson et al. [7] showed that vortices may be generated by movement of a localised potential through a condensate, while Marzlin and Zhang [8] investigated vortex production using four laser beams in a ring configuration. A potentially important scheme for vortex detection using phase sensitive detection was formulated by Bolda and Walls [9]. Experimental realisation of vortices has now been achieved by the JILA group in a two-component condensate [10], in confirmation of a theoretical prediction by Williams and Holland [11], and also by Madison et al. [12] who reported the first observation of vortices in a single-component condensate.