The coherent nonlinear tunneling dynamics of a boson-fermion mixture in a double-well potential is studied in this paper. Four types of phase are found for the mixture. The first one is two species localizing in different potential wells. The second one is two species coexisting in the same well. The third one is two species equally populated in two wells. The fourth one is one species equally populated in two wells while the other species is in one well. The phase transitions among these four states have been investigated. The interspecies and intraspecies interactions as well as bosonic and fermionic numbers can dramatically affect these phase transitions.
In this paper, we study the role of both "spin"(species) and mass imbalance in a mixture of two species of fermionic atoms with attractive interaction in an one-dimensional optical lattice. Using the bosonization approach, quantum phase transitions between a liquid phase and phase separated states are studied under various conditions of interaction, spin imbalance, and mass imbalance. We find that, in the phase-separated region, there exists two kinds of phase separation and a special quantum phase transition might exist between them in the large
U limit. On the other hand, the singlet superconducting correlation dominates in the liquid phase. The pairing behavior has been also demonstrated that there is oscillating behavior in real space. We find both the spin and mass imbalance are in favor of the formation of Fulde-Ferrell-Larkin-Ovchinnikov state.
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.