Anisotropic potential immersed in a dipolar Bose-Einstein condensate

TL;DR

This paper investigates how a static impurity interacts with an anisotropic dipolar Bose-Einstein condensate, revealing that the impurity adapts its shape to align with the dipolar medium's anisotropy, using analytical and numerical methods.

Contribution

It introduces a modified Gross-Pitaevskii equation for impurity behavior in dipolar BECs and analyzes the impurity's shape adaptation to anisotropic interactions.

Findings

Impurity prefers to align with dipole direction.

Impurity shape changes to match medium anisotropy.

Numerical and analytical methods confirm impurity behavior.

Abstract

We study a modified three-dimensional Gross-Pitaevski equation that describes a static impurity in a dipolar Bose-Einstein condensate (BEC). Our focus is on the interplay between the shape of the impurity and the anisotropy of the medium manifested in the energy and the density of the system. Without external confinement, properties of the system are derived with basic analytical approaches. For a system in a harmonic trap, the model is investigated numerically, using the split-step Crank-Nicolson method. Our results demonstrate that the impurity would prefer to change its shape to accommodate the anisotropic character of the bath, in particular it would prefer to align itself with the direction of the dipoles. Our work complements studies of impurities in Bose gases with zero-range interactions, and paves the way for studies of dipolar polarons with a modified Gross-Pitaevski equation.