Static interfacial properties of Bose-Einstein condensate mixtures

TL;DR

This paper investigates the static interfacial properties of phase-separated Bose-Einstein condensate mixtures, deriving exact and approximate analytical expressions for interfacial tension and exploring wetting phenomena at optical walls.

Contribution

It introduces a double-parabola approximation model that simplifies GP theory while accurately capturing interfacial physics and provides analytical formulas for interfacial tension.

Findings

Exact solution for specific GP equations case.

DPA model yields accurate interfacial tension expressions.

Wetting phase boundary closely matches GP theory results.

Abstract

Interfacial profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates are studied theoretically. The two condensates are characterized by their respective healing lengths $\xi_1$ and $\xi_2$ and by the inter-species repulsive interaction $K$. An exact solution to the Gross-Pitaevskii (GP) equations is obtained for the special case $\xi_2/\xi_1 = 1/2$ and $K = 3/2$. Furthermore, applying a double-parabola approximation (DPA) to the energy density featured in GP theory allows us to define a DPA model, which is much simpler to handle than GP theory but nevertheless still captures the main physics. In particular, a compact analytic expression for the interfacial tension is derived that is useful for all $\xi_1, \xi_2$ and $K$. An application to wetting phenomena is presented for condensates adsorbed at an optical wall. The wetting phase boundary obtained within the DPA model nearly coincides with the exact one in GP theory.