Abstract
We show that, depending on the ratio between the inter- and the intra-species interactions, a binary mixture trapped in a three-well potential with periodic boundary conditions exhibits three macroscopic ground-state configurations which differ in the degree of mixing. Accordingly, the corresponding quantum states feature either delocalization or a Schrödinger cat-like structure. The two-step phase separation occurring in the system, which is smoothed by the activation of tunnelling processes, is confirmed by the analysis of the energy spectrum that collapses and rearranges at the two critical points. In such points, we show that also Entanglement Entropy, a quantity borrowed from quantum-information theory, features singularities, thus demonstrating its ability to witness the double mixining-demixing phase transition. The developed analysis, which is of interest to both the experimental and theoretical communities, opens the door to the study of the demixing mechanism in complex lattice geometries.
Highlights
Spatial phase separation of the atomic species forming a binary bosonic mixture represents a rather intuitive phenomenon in which a sufficiently strong inter-species repulsion is able to localize the two components in separated domains breaking the spatial symmetry of the system
In addition to highlight how phase separation is marked by the spectral collapse of energy levels, this study reproduces, in the presence of large boson numbers, the well known critical value W/U = 1 characterizing the spatial separation in large-size lattices at zero temperature18
The model describing a binary mixture in a triple well is effectively represented by two Bose-Hubbard Hamiltonians, each one associated to a single component and depending on three spatial boson modes, and by the density-density interspecies coupling of the two components
Summary
Spatial phase separation of the atomic species forming a binary bosonic mixture represents a rather intuitive phenomenon in which a sufficiently strong inter-species repulsion is able to localize the two components in separated domains breaking the spatial symmetry of the system. This phase transition has attracted considerable attention within the physics of binary condensates and the mechanism of phase separation, investigated in the condensate mean-field picture, has revealed a nontrivial dependence from trapping potentials, the boson number of each species and other significant parameters of the system.
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