Pure Fulde-Ferrell-Larkin-Ovchinnikov state in optical lattices

We study the phase diagram of a one-dimensional, two-component attractive fermions on optical lattices in an off-diagonal confinement. We identify in this system a pure Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with spatially modulated superfluidity and polarization in a large parameter window, which provides an easier playground to detect the FFLO state experimentally. The clear signature of FFLO state is analyzed in the ground state properties, the pair correlation functions, and the magnetic structure factor, using the density-matrix renormalization group method.