A continuous-variable approach to the spectral properties and quantum states of the two-component Bose-Hubbard dimer

Abstract

A bosonic gas formed by two interacting species trapped in a double-well potential features macroscopic localization effects when the interspecies interaction becomes sufficiently strong. A repulsive interaction spatially separates the species into different wells while an attractive interaction confines both species in the same well. We perform a fully-analytic study of the transitions from the weak- to the strong-interaction regime by exploiting the semiclassical method in which boson populations are represented in terms of continuous variables. We find an explict description of low-energy eigenstates and spectrum in terms of the model parameters which includes the neighborhood of the transition point. To test the effectiveness of the continuous-variable method we compare its predictions with the exact results found numerically. Numerical calculations confirm the spectral collapse evidenced by this method when the space localization takes place.

13 pages, 8 figures

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• The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer
• Residual entropy and critical behavior of two interacting boson species in a double well
• Interference, spectral momentum correlations, entanglement, and Bell inequality for a trapped interacting ultracold atomic dimer: Analogies with biphoton interferometry
• Spatial Phase Separation of a Binary Mixture in a Ring Trimer