Dipolar Bose-Einstein Condensates in Weak Anisotropic Disorder

TL;DR

This paper analytically investigates how weak anisotropic disorder affects the properties of dipolar Bose-Einstein condensates, revealing anisotropic behaviors and condensate fragmentation due to disorder correlations.

Contribution

It provides the first perturbative analytic results for dipolar BECs in anisotropic Lorentzian disorder, extending previous contact interaction models to include anisotropic disorder effects.

Findings

Disorder causes anisotropic depletion of condensate and superfluid densities.

Results are consistent with Gaussian disorder in isotropic cases.

Anisotropic disorder leads to fragmented condensate formation.

Abstract

Here we study properties of a homogeneous dipolar Bose-Einstein condensate in a weak anisotropic random potential with Lorentzian correlation at zero temperature. To this end we solve perturbatively the Gross-Pitaevskii equation to second order in the random potential strength and obtain analytic results for the disorder ensemble averages of both the condensate and the superfluid depletion, the equation of state, and the sound velocity. For a pure contact interaction and a vanishing correlation length, we reproduce the seminal results of Huang and Meng, which were originally derived within a Bogoliubov theory around a disorder-averaged background field. For dipolar interaction and isotropic Lorentzian-correlated disorder, we obtain results which are qualitatively similar to the case of an isotropic Gaussian-correlated disorder. In the case of an anisotropic disorder, the physical observables show characteristic anisotropies which arise from the formation of fragmented dipolar condensates in the local minima of the disorder potential.