Impurity crystal in a Bose-Einstein condensate

TL;DR

This paper explores how impurity fields in a Bose-Einstein condensate can localize, interact, and form a crystalline structure exhibiting supersolid properties, advancing understanding of impurity behavior in quantum fluids.

Contribution

It introduces a model for impurity interactions mediated by a condensate, demonstrating spontaneous impurity crystal formation and supersolid behavior in Bose-Einstein condensates.

Findings

Impurity fields can localize within the condensate.

Impurities attract each other via condensate-mediated interactions.

Impurity crystals exhibit nonclassical rotational inertia, indicating supersolidity.

Abstract

We investigate the behavior of impurity fields immersed in a larger condensate field in 1, 2, and 3 dimensions. We discuss the localization of a single impurity field within a condensate and note the effects of surface energy. We derive the functional form of the attractive interaction between two impurities due to mediation from the condensate. Generalizing the analysis to $N$ impurity fields, we show that within various parameter regimes a crystal of impurity fields can form spontaneously in the condensate. Finally, the system of condensate and crystallized impurity structure is shown to have nonclassical rotational inertia, which is characteristic of superfluidity, i.e. the system can be seen to exhibit supersolid behavior.