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We study the interplay between the long- and short-range interaction of aone-dimensional optical lattice system of two-component dipolar fermions byusing the density matrix renormalization group method. The atomic densityprofile, pairing-pairing correlation function, and the compressibility arecalculated in the ground state, from which we identify the parameter region ofthe Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing state, half-metal (HM)state, FFLO-HM state, and the normal polarized state, and thus the phasediagram in the coordinates of the long- and short-range interaction strength.The effect of the long-range dipolar interaction on the FFLO state is discussedin details. We find that the long-range part of the dipole-dipole interactiondoes not sweep away the FFLO superconducting region that is driven by theshort-range interaction in the Hubbard model, and thus the FFLO state survivesin the wide parameter space of the long-range interaction, polarization and thefilling.

Fulde-Ferrell-Larkin-Ovchinnikov pairing states of a polarized dipolar Fermi gas trapped in a one-dimensional optical lattice