Current-induced instability of superfluid Fermi gases in optical lattices

We study the stability of superfluid flow of two-component Fermi gases in one-dimensional optical lattices. We find that the density fluctuation mode, the so-called Anderson-Bogoliubov mode, has the roton-like structure as seen in superfluid ⁴He. With increasing supercurrent, one of the roton-like minima reaches zero before the pair breaking occurs. This means that the instability of the superfluid Fermi gas is due to the spontaneous emission of the roton-like excitations of the Anderson-Bogoliubov mode instead of due to the Cooper pair breaking. We calculate the critical velocity determined by the roton-like structure for one-dimensional optical lattices.