Abstract
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 with 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.
Highlights
Systems formed by gases of ultracold bosons trapped in homogenous arrays of potential wells [1] have attracted, in the last two decades, an enormous amount of attention due to the rich variety of phenomena they feature at zero temperature [2,3]
In Ref. [16], we showed that the two-species dimer (TSD) manifests non trivial entanglement properties in the ground-state suggesting the presence of a bipartite residual entropy at T = 0
This can be naturally done by extending the definition of entanglement entropy Equation (5) at finite T in the way suggested by the expression for the equilibrium entropy Equation (8)
Summary
Systems formed by gases of ultracold bosons trapped in homogenous arrays of potential wells (optical lattices) [1] have attracted, in the last two decades, an enormous amount of attention due to the rich variety of phenomena they feature at zero temperature [2,3]. The critical behavior of the TSD has been confirmed by resorting to quantum-correlation indicators such as the Fisher information, the coherence visibility and the entanglement entropy (EE) The latter, in particular, has proved sensitive in detecting the macroscopic changes in the ground-state structure both for repulsive and for attractive interspecies interaction. After the realization of optical lattices trapping ultracold atoms, it has become more and more evident that reducing (and measuring) the temperature on the nanoscale is an outstanding problem [18] For this reason, the detection of zero-temperature phase transitions such as the space separation in bosonic mixtures (or its simpler dimer version, the DL transition) must more realistically rely on indicators which are reminescent of the critical behavior of the system even when temperature is non-zero [19].
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