Collisionally inhomogeneous Bose-Einstein condensates in double-well potentials

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) types of interparticle interactions. Our analysis is based on the continuation of the symmetric ground state and anti-symmetric first excited state of the non-interacting (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, 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. (C) 2008 Elsevier B.V. All rights reserved.