Abstract 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 23Na + 39K, thanks to the large tunability of their intra- and inter-species scattering lengths.
We investigated the spatial phase separation of the two components forming a bosonic mixture distributed in a four-well lattice with a ring geometry. We studied the ground state of this system, described by means of a binary Bose–Hubbard Hamiltonian, by implementing a well-known coherent-state picture which allowed us to find the semi-classical equations determining the distribution of boson components in the ring lattice. Their fully analytic solutions, in the limit of large boson numbers, provide the boson populations at each well as a function of the interspecies interaction and of other significant model parameters, while allowing to reconstruct the non-trivial architecture of the ground-state four-well phase diagram. The comparison with the L-well (L=2,3) phase diagrams highlights how increasing the number of wells considerably modifies the phase diagram structure and the transition mechanism from the full-mixing to the full-demixing phase controlled by the interspecies interaction. Despite the fact that the phase diagrams for L=2,3,4 share various general properties, we show that, unlike attractive binary mixtures, repulsive mixtures do not feature a transition mechanism which can be extended to an arbitrary lattice of size L.
We investigate the phase separation mechanism of bosonic binary mixtures in spatially-fragmented traps, evidencing the emergence of phases featuring a different degree of mixing. The analysis is initially carried out by means of a semiclassical approach which transparently shows the occurrence of critical phenomena. These predictions are actually corroborated by the study of genuinely quantum indicators, including, but not limited to, the energy levels' structure and the entanglement between the species. The scope of our work goes also beyond the ground state's properties, as it comprises excited states and the dynamical evolution thereof. In particular, after introducing an indicator to monitor the degree of mixing, we show that several dynamical regimes feature persistent demixing in spite of their remarkably chaotic character.
We investigate the mechanism of formation of supermixed solitonlike states in bosonic binary mixtures loaded in ring lattices. We evidence the presence of a common pathway which, irrespective of the number of lattice sites and upon variation of the interspecies attraction, leads the system from a mixed and delocalized phase to a supermixed and localized one, passing through an intermediate phase where the supermixed soliton progressively emerges. The degrees of mixing, localization, and quantum correlation of the two condensed species, quantified by means of suitable indicators commonly used in statistical thermodynamics and quantum information theory, allow one to reconstruct a bidimensional mixing-supermixing phase diagram featuring two characteristic critical lines. Our analysis is developed both within a semiclassical approach capable of capturing the essential features of the two-step mixing-demixing transition and with a fully quantum approach.
This thesis investigates bosonic mixtures in ultra-cold atom systems. We mainly focus on mixtures of two bosonic twin-species trapped in optical lattices, paying particular attention to the properties of spatial separation. The study is carried out by means of the path-integral quantum Monte Carlo by the two-worm algorithm and by analytical calculations where the complexity of the system allows it. The mixture is trapped in a square optical lattice at different filling and temperature conditions. We explore the ground-state phase diagram showing that various quantum phases can arise depending on the interplay between intra- and inter-species interactions. Demixed phases, characterized by spatial separation of the two species, are studied in details determining under which conditions they can be stabilized. The influence of temperature, filling factor and harmonic trap on phase separation is also investigated. An interesting dependence of the degree of demixing from temperature has been found, suggesting new ways to measure the temperature of a two-component bosonic mixture. We also study spatial phase separation in the simple case of a two-component mixture in a double-well potential both numerically and by means of the Bogoliubov approximaton. We show that even in this simple case the main features of the mixing/ demixing phase transitions are observed, and that the transition is characterized by a spectral collapse of the energy eigenvalues reflecting the dramatic change of algebraic structure of the model.
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.