2008/11/09 by C. Wang, Chen Wang, P. G. Kevrekidis +5 · 11 citations
Physics and Astronomy · #Bifurcation #Bose–Einstein condensate #Classical mechanics #Cold Atom Physics and Bose-Einstein Condensates #Excited state #Geometry #Mathematical analysis #Monotonic function #Nonlinear system #Optical properties and cooling technologies in crystalline materials #Physics #Quantum mechanics #Saddle #Saddle point #Strong Light-Matter Interactions #nlin.PS
paper · pdf · doi:10.1016/j.physd.2008.11.003
published in Physica D Nonlinear Phenomena 238(15), 1362-1371 (Elsevier BV) · 14 pages, 12 figures, Physica D, in press
arxiv created 2008/11/09 · openalex publication_date 2008/11/26 · arxiv updated 2015/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.