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We study through controlled numerical simulation the ground state propertiesof spin-polarized strongly interacting fermi gas in an anisotropic opticallattice, which is described by an effective one-dimensional general Hubbardmodel with particle correlated hopping rate. We show that theFulde-Ferrell-Larkin-Ovchinnikov (FFLO) type of state, while enhanced by anegative correlated hopping rate, can be completely suppressed by positiveparticle correlated hopping, yielding to an unusual magnetic phase even forparticles with on-site attractive interaction We also find several differentphase separation patterns for these atoms in an inhomogeneous harmonic trap,depending on the correlated hopping rate.

Suppression or enhancement of the Fulde-Ferrell-Larkin-Ovchinnikov order in a one-dimensional optical lattice with particle correlated tunnelling