Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions

TL;DR

This paper derives and analyzes simplified one- and two-dimensional mean-field equations for trapped dipolar Bose-Einstein condensates, revealing how dipolar interactions influence condensate shape and anisotropy.

Contribution

The paper introduces rigorous reduced-dimensional mean-field equations for dipolar BECs with arbitrary polarization, including anisotropic nonlocal potentials, and validates them against full Gross-Pitaevskii solutions.

Findings

Reduced equations accurately predict condensate profiles

Dipolar interactions modify contact interactions and induce anisotropy

Analytical density profiles match numerical solutions

Abstract

We derive rigorous one- and two-dimensional mean-field equations for cigar- and pancake-shaped dipolar Bose-Einstein condensates with arbitrary polarization angle. We show how the dipolar interaction modifies the contact interaction of the strongly confined atoms. In addition, our equations introduce a nonlocal potential, which is anisotropic for pancake-shaped condensates. We propose to observe this anisotropy via measurement of the condensate aspect ratio. We also derive analytically approximate density profiles from our equations. Both the numerical solutions of our reduced mean-field equations and the analytical density profiles agree well with numerical solutions of the full Gross-Pitaevskii equation while being more efficient to compute.