  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.
