The effect of s-wave scattering length on self-trapping and tunneling phenomena of Fermi gases in one-dimensional accelerating optical lattices

We investigate the tunneling dynamics of the Fermi gases in an optical lattice in the Bose-Einstein condensation (BEC) regime. The three critical scattering lengths and the system energies are found in different cases of Josephson oscillation (JO), oscillating-phase-type self-trapping (OPTST), running-phase-type self-trapping (RPTST), and self-trapping (ST). It is found that the s-wave scattering lengths have a crucial role on the tunneling dynamics. By adjusting the scattering length in the adiabatic condition, the transition probability changes with the adiabatic periodicity and a rectangular periodic pattern emerges. The periodicity of the rectangular wave depends on the system parameters such as the periodicity of the adjustable parameter, the s-wave scattering length.