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

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 ξ1 and ξ2. The inter-atomic interactions are repulsive. In particular, the reduced 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.