Induced interaction and crystallization of self-localized impurity fields in a Bose-Einstein condensate

TL;DR

This paper models impurity fields in a Bose-Einstein condensate, revealing various phases including a crystalline structure that exhibits superfluidity, thus providing insights into impurity interactions and supersolid behavior.

Contribution

It analytically derives impurity-impurity interactions mediated by the condensate and explores the phase diagram, including a novel crystalline phase of impurity fields.

Findings

Identification of four distinct impurity phases.

Derivation of impurity-impurity attractive tail.

Prediction of a superfluid crystalline phase.

Abstract

We model the behavior of N classical impurity fields immersed in a larger Bose-Einstein condensate by N+1 coupled nonlinear Schrodinger equations in 1, 2, and 3 space dimensions. We discuss the stability of the uniform miscible system and show the importance of surface tension for self localization of the impurity fields. We derive analytically the attractive tail of impurity-impurity interaction due to mediation by the underlying condensate. Assuming all impurity fields interact with the same strength, we explore the resulting phase diagram, which contains four phases: {\it I}) all fields are miscible; {\it II}) the impurity fields are miscible with each other but phase separate from the condensate as a single bubble; {\it III}) the localized impurity fields stay miscible with the condensate, but not with each other; and {\it IV}) the impurity fields phase separate from the condensate and each other, forming a crystalline structure within a bubble. Thus, we show that a crystal can be constructed solely from superfluid components. Finally, we argue that the crystalline phases maintain their superfluid behavior, i.e. they possess a nonclassical rotational inertia, which, combined with lattice order, is a characteristic of supersolidity.