Variational Analyze Of Gap Soliton Of Superfluid Fermion Gas In Optical Lattice

Studies of superfluid Fermi gases in optical lattices have been become an interesting subject in physics. In experiment, the interaction can be switched from repulsion to attraction by applying magnetic field near the Feshbach resonance. Use this technique, it's physical parameters, e.g., lattice parameters, interaction strength, ect, can be manipulated. Although in resent years the studies of self-trapping, stability, gap of two atoms about superfluid fermion gas, the gap soliton in optical lattices about superfluid fermion gas was needed further discussion, so did in this work.In this letter we consider adequate atoms of 6Li of superfluid Fermi gas in 1D or 2D lattices, and the spatial scales between atoms far less than the lattice scale. The system based on the hydrodynamic model and mean-field theory, and was switched from molecule BEC to BCS superfluidity at zero temperature, we got the relation between nonlinear interactions, chemical potential and optical lattice by variational approximation (VA). The relation was the important conditions of distributing and existence of gap solitons, and it was different from superfluid BCS to molecule BEC. The existence of superfluid Fermi gas of gap solitons were found by VA, and the distributing of gap solitons were obvious different from superflid BCS to molecule BEC. it can provide a higher accuracy distributing of superfluid Fermi gas of gap solitons except for very colse to edges of bandgaps producing undulating tailsby VA.The objective of this work was to predict the existence of quasi-1D and quasi-2D solitons in the BCS superfluid formed by a gas of fermion atoms, and we discussed the gap solitons have the different distributing from superfluid Fermi BCS to molecule BEC by VA. In a word, our work is meaningful to understand the properties of dynamics of superfluid Fermi gas in optical lattices.