Bose-Einstein Condensation Temperature of Dipolar Gas in Anisotropic Harmonic Trap

TL;DR

This paper calculates how dipole-dipole interactions in an anisotropic harmonic trap affect the Bose-Einstein condensation temperature, identifying conditions where the shift vanishes and how experimental parameters can enhance this effect.

Contribution

It provides a perturbative calculation of the temperature shift due to dipolar interactions in anisotropic traps, including the identification of magic angles and parameter dependencies.

Findings

Dipolar interactions cause a measurable shift in BEC temperature.

Magic angles exist where the dipolar shift cancels out.

Increasing particle number and trap anisotropy enhances the dipolar shift.

Abstract

We consider a dilute gas of dipole moments in an arbitrary harmonic trap and treat both the short-range, isotropic delta-interaction and the long-range, anisotropic dipole-dipole interaction perturbatively. With this we calculate the leading shift of the critical temperature with respect to that of an ideal gas as a function of the relative orientation of the dipole moments with respect to the harmonic trap axes. In particular, we determine those magic angles, where the dipolar shift of the Bose-Einstein condensation temperature vanishes. Furthermore, we show for the parameters of the ongoing 52Cr-experiment in Stuttgart that this dipolar shift can be enhanced by increasing the number of particles, the geometrical mean trap frequency, and the anisotropy of the trap.