On an exact solution of the Thomas-Fermi equation for a trapped Bose-Einstein condensate with dipole-dipole interactions

TL;DR

This paper presents an exact analytical solution to the Thomas-Fermi equation for a dipolar Bose-Einstein condensate in a harmonic trap, revealing that the condensate's density profile remains an inverted parabola despite anisotropic dipolar interactions.

Contribution

It provides the first exact solution to the Thomas-Fermi equation incorporating both dipole-dipole and contact interactions in a harmonic trap.

Findings

The density profile remains an inverted parabola with a modified aspect ratio.

Dipolar interactions influence electrostriction and stability properties.

The solution simplifies understanding of dipolar BECs in harmonic traps.

Abstract

We derive an exact solution to the Thomas-Fermi equation for a Bose-Einstein condensate which has dipole-dipole interactions as well as the usual s-wave contact interaction, in a harmonic trap. Remarkably, despite the non-local anisotropic nature of the dipolar interaction the solution is an inverted parabola, as in the pure s-wave case, but with a different aspect ratio. Various properties such as electrostriction and stability are discussed.