Statics and dynamics of BEC's in double square well potentials

TL;DR

This paper analyzes the behavior of Bose-Einstein condensates in double square well potentials, exploring symmetry breaking, bifurcations, and dynamics using analytical and Josephson junction models.

Contribution

It introduces a method to obtain all solutions for repulsive interactions and analytically finds the bifurcation point for symmetry breaking in double well potentials.

Findings

Symmetry breaking solutions exist at strong nonlinearity.

Bifurcation points are analytically determined.

New phenomena occur with wells of different depths.

Abstract

In this paper we treat the behavior of Bose Einstein condensates in double square well potentials, both of equal and different depths. For even depth, symmetry preserving solutions to the relevant nonlinear Schr\"{o}dinger equation is known, just as in the linear limit. When the nonlinearity is strong enough, symmetry breaking solutions also exist, side by side with the symmetric one. Interestingly, solutions almost entirely localized in one of the wells are known as an extreme case. Here we outline a method for obtaining all these solutions for repulsive interactions. The bifurcation point at which, for critical nonlinearity, the asymmetric solutions branch off from the symmetry preserving ones is found analytically. We also find this bifurcation point and treat the solutions generally via a Josephson Junction model. When the confining potential is in the form of two wells of different depth, interesting new phenomena appear. This is true of both the occurrence of the bifurcation point for the static solutions, and also of the dynamics of phase and amplitude varying solutions. Again a generalization of the Josephson model proves useful. The stability of solutions is treated briefly.