Exact hydrodynamics of a trapped dipolar Bose-Einstein condensate

TL;DR

This paper derives the exact density profile of a trapped dipolar Bose-Einstein condensate in the Thomas-Fermi limit, showing it maintains an inverted parabola shape with a modified aspect ratio despite anisotropic dipolar interactions.

Contribution

It provides the exact density profile and shape oscillation frequencies for a dipolar BEC, extending the scaling solution approach to include dipolar interactions.

Findings

Density profile remains an inverted parabola with modified aspect ratio.

Scaling solutions apply to dipolar BECs for shape oscillations.

Exact monopole and quadrupole oscillation frequencies obtained.

Abstract

We derive the exact density profile of a harmonically trapped Bose-Einstein condensate (BEC) which has dipole-dipole interactions as well as the usual s-wave contact interaction, in the Thomas-Fermi limit. Remarkably, despite the non-local anisotropic nature of the dipolar interaction, the density turns out to be an inverted parabola, just as in the pure s-wave case, but with a modified aspect ratio. The ``scaling'' solution approach of Kagan, Surkov, and Shlyapnikov [Phys. Rev. A 54, 1753 (1996)] and Castin and Dum [Phys. Rev. Lett. 77}, 5315 (1996)] for a BEC in a time-dependent trap can therefore be applied to a dipolar BEC, and we use it to obtain the exact monopole and quadrupole shape oscillation frequencies.