Residual entropy and critical behavior of two interacting boson species in a double well

Motivated by the importance of entanglement and correlation indicators in the analysis of quantum systems, we study the equilibrium and the bipartite residual entropy in a two-species Bose Hubbard dimer when the spatial phase separation of the two species takes place. We consider both the zero and non-zero-temperature regime. We present different kinds of residual entropies (each one associated to a different way of partitioning the system), and we show that they strictly depend on the specific quantum phase characterizing the two species (supermixed, mixed or demixed) even at finite temperature. To provide a deeper physical insight into the zero-temperature scenario, we apply the fully-analytical variational approach based on su(2) coherent states and provide a considerably good approximation of the entanglement entropy. Finally, we show that the effectiveness of bipartite residual entropy as a critical indicator at non-zero temperature is unchanged when considering a restricted combination of energy eigenstates.Comment: 18 pages, 9 figure

The phase-separation mechanism of a binary mixture in a ring trimer

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 Schr\"odinger 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.Comment: 14 pages, 9 figure

The mixing-demixing phase diagram of ultracold heteronuclear mixtures in a ring trimer

We derive the complete mixing-demixing phase-diagram relevant to a bosonic binary mixture confined in a ring trimer and modeled within the Bose-Hubbard picture. The mixing properties of the two quantum fluids, which are shown to be strongly affected by the fragmented character of the confining potential, are evaluated by means of a specific indicator imported from Statistical Thermodynamics and are shown to depend only on two effective parameters incorporating the asymmetry between the heteronuclear species. To closely match realistic experimental conditions, our study is extended also beyond the pointlike approximation of potential wells by describing the systems in terms of two coupled Gross-Pitaevskii equations. The resulting mean-field analysis confirms the rich scenario of mixing-demixing transitions of the mixture and also constitutes an effective springboard towards a viable experimental realization. We additionally propose an experimental realization based on a realistic optical-tweezers system and on the bosonic mixture 23 Na + 39 K, thanks to the large tunability of their intra- and inter-species scattering lengths. © 2019, The Author(s)