We numerically determine the very rich phase diagram of mass-imbalanced binary mixtures of hardcore bosons (or equivalently —fermions, or hardcore Bose/Fermi mixtures) loaded in one-dimensional optical lattices. Focusing on commensurate fillings away from half-filling, we find a strong asymmetry between attractive and repulsive interactions. Attraction is found to always lead to pairing, associated with a spin gap, and to pair crystallization for very strong mass imbalance. In the repulsive case the two atomic components remain instead fully gapless over a large parameter range; only a very strong mass imbalance leads to the opening of a spin gap. The spin-gap phase is the precursor of a crystalline phase occurring for an even stronger mass imbalance. The fundamental asymmetry of the phase diagram is at odds with recent theoretical predictions, and can be tested directly via time-of-flight experiments on trapped cold atoms.
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.