Exotic superfluids are characterized by the coexistence of superconductivity and magnetism. In fermionic systems superfluidity is achieved by pairing of particles while magnetization is induced by an imbalanced population of two species of fermions. This exotic coexistence, first investigated by Fulde and Ferrell and Larkin and Ovchinnikov (FFLO), is predicted to show distinct properties in comparison to a conventional BCS superfluid. Experimentally, the FFLOstate has been investigated in cold atoms experiments by several groups (Ketterle, Hulet, Törmä). From the theoretical point of view, the Hubbard model has been used to investigate the FFLO properties and to predict the regimes where the FFLO state appears. In this talk we will discuss theoretical results for the 1D Hubbard lattice with spinimbalanced populations. In particular, we have obtained an analytical expression for the critical polarization below which the FFLO state emerges and depicted the phase diagram as a function of interaction and particle density. We have also investigated i) the effects of the experimental harmonic trap, ii) the local magnetization, iii)the behavior of entanglement, and iv) the spinflip channels which favor the pairing protection. We find that beyond the FFLOstate regime the spinflip processes trigger a breaking pairs avalanche, leading the system to the normal (non superfluid) polarized phase.
