Vortex–Antivortex Unbinding in Inhomogeneous 2D Atomic Condensates

Abstract

The breakdown of superfluidity in a two-dimensional Bose gas is linked with the unbinding of vortex–antivortex pairs, which has been observed directly in a recent experiment with trapped atomic gases. The phenomenological Kosterlitz–Thouless (KT) description of the dissociation process, originally set up in the context of a uniform Bose system (such as superfluid helium), is no longer suited in the case of a strongly inhomogenous atomic gas in which, moreover, the vortex core size is a non-negligible fraction of the cloud size. Using the Gross–Pitaevskii energy functional we extend the original KT argument to take into account inhomogeneity and vortex core size in the calculation of both the binding energy of the vortex–antivortex pair, and the entropy per vortex in the cloud. We derive the resulting shift in the KT temperature, and find that it is in good agreement with experiment, in contrast to the value obtained in the context of the uniform Bose gas. Finally, we look at different intermediate levels of approximation for the binding energy and the entropy and investigate their effect on the shift in the KT temperature.