Bose-Einstein condensation in variable dimensionality

Abstract

We introduce dimensional perturbation techniques to Bose-Einstein condensation of inhomogeneous alkali-metal gases. The perturbation parameter is $\ensuremath{\delta}=1/\ensuremath{\kappa},$ where $\ensuremath{\kappa}$ depends on the effective dimensionality of the condensate and on the angular momentum quantum number. We derive a simple approximation that is more accurate and flexible than the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ Thomas-Fermi ground-state approximation of the Gross-Pitaevskii equation. The approximation presented here is well suited for calculating properties of states in three dimensions and in low-effective dimensionality, such as vortex states in a highly anisotropic trap.