Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials

TL;DR

This paper investigates how spatially varying interactions in quasi-one-dimensional Bose-Einstein condensates within double-well potentials lead to unique bifurcation phenomena and altered ground state properties, expanding understanding of nonlinear quantum systems.

Contribution

It introduces the analysis of collisionally inhomogeneous BECs in double wells, revealing novel bifurcation scenarios and solution branch behaviors not seen in standard models.

Findings

Collisionally inhomogeneous interactions cause saddle-node bifurcations.

Stronger inhomogeneity leads to the disappearance of certain solution branches.

A branch changes monotonicity depending on the chemical potential and nonlinearity sign.

Abstract

In this work, we consider quasi-one-dimensional Bose-Einstein condensates (BECs), with spatially varying collisional interactions, trapped in double well potentials. In particular, we study a setup in which such a 'collisionally inhomogeneous' BEC has the same (attractive-attractive or repulsive-repulsive) or different (attractive-repulsive) type of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the noninteracting (linear) limit into their nonlinear counterparts. The collisional inhomogeneity produces a saddle-node bifurcation scenario between two additional solution branches; as the inhomogeneity becomes stronger, the turning point of the saddle-node tends to infinity and eventually only the two original branches remain present, which is completely different from the standard double-well phenomenology. Finally, one of these branches changes its monotonicity as a function of the chemical potential, a feature especially prominent, when the sign of the nonlinearity changes between the two wells. Our theoretical predictions, are in excellent agreement with the numerical results.