Interfacial tension and wall energy of a Bose-Einstein condensate binary mixture: triple-parabola approximation

TL;DR

This paper introduces a triple-parabola approximation (TPA) for analyzing interfacial properties of binary Bose-Einstein condensates, providing more accurate analytic expressions for interfacial tension and wall energy than previous models.

Contribution

The paper develops a novel triple-parabola approximation that improves analytic modeling of interfacial tension and wall energy in binary BEC mixtures over existing double-parabola methods.

Findings

More accurate interfacial tension expressions derived.

Enhanced agreement with Gross-Pitaevskii theory predictions.

Qualitative improvements in interface profile modeling.

Abstract

Accurate and useful analytic approximations are developed for order parameter profiles and interfacial tensions of phase-separated binary mixtures of Bose-Einstein condensates. The pure condensates 1 and 2, each of which contains a particular species of atoms, feature healing lengths $\xi_1$ and $\xi_2$. The inter-atomic interactions are repulsive. In particular, the effective inter-species repulsive interaction strength is $K$. A triple-parabola approximation (TPA) is proposed, to represent closely the energy density featured in Gross-Pitaevskii (GP) theory. This TPA allows us to define a model, which is a handy alternative to the full GP theory, while still possessing a simple analytic solution. The TPA offers a significant improvement over the recently introduced double-parabola approximation (DPA). In particular, a more accurate amplitude for the wall energy (of a single condensate) is derived and, importantly, a more correct expression for the interfacial tension (of two condensates) is obtained, which describes better its dependence on $K$ in the strong segregation regime, while also the interface profiles undergo a qualitative improvement.