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.

arXiv comment13 pages, 8 figures

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• Two-species boson mixture on a ring: A group theoretic approach to the quantum dynamics of low-energy excitations
• Phase separation can be stronger than chaos
• The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer
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• Residual entropy and critical behavior of two interacting boson species in a double well
• The phase-separation mechanism of a binary mixture in a ring trimer
• 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
• A binary mixture of Bose-Einstein-condensates in a double-well potential: Berry phase and two-mode entanglement