  The paper is devoted to a study of superconducting properties of
population-imbalanced fermionic mixtures in quasi-one dimensional optical
lattices. The system can be effectively described by the attractive Hubbard
model with the Zeeman magnetic field term. We investigated the ground state
phase diagram of the model as a function of the chemical potential and the
magnetic field. The ground state of the system exhibits the conventional
BCS-type superconductivity as well as the unconventional so-called
Fulde-Ferrell-Larkin-Ovchinnikov state, in which the total momentum of Cooper
pairs is non-zero. We determine the orders of transitions as well as the
behavior of order parameters with a change of the model parameters.
