Sound waves and dynamics of superfluid Fermi gases in optical lattices

The sound waves, the stability of Bloch waves, the Bloch oscillation, and the self-trapping phenomenon in interacting two-component Fermi gases throughout the BEC-BCS crossover in one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) optical lattices are discussed in detail. Within the hydrodynamical theory and by using the perturbative and tight-binding approximation, sound speed in both weak and tight 1D, 2D, 3D optical lattices, and the criteria for occurrences of instability of Bloch waves and self-trapping of Fermi gases along the whole BEC-BCS crossover in tight 1D, 2D, 3D optical lattices are obtained analytically. The results show that the sound speed, the criteria for occurrences of instability of Bloch waves and self-trapping, and the destruction of Bloch oscillation are modified dramatically by the lattice parameters (lattice dimension and lattice strength), the atom density or atom number, and the atom interaction.