Bethe-Salpeter equations for the collective-mode spectrum of a superfluid Fermi gas in a moving optical lattice

摘要

We derive the Bethe-Salpeter (BS) equations for the collective-mode spectrumof superfluid Fermi gases of equal mixture of atomic Fermi gas of two hyperfinestates loaded into a moving optical lattice. In a moving lattice the superfluidstate is unstable due to spontaneous emission of the short-wavelength rotonlikeexcitations which appear in the spectrum of the collective modes. It is shownthat the spectrum obtained by the BS equations is in an excellent agreementwith the collective-mode dispersion calculated by the perturbation approach,while there are some differences between the results obtained by densityresponse function method and by the BS approach. The difference increases withincreasing the lattice velocity, which can be seen in the analyticalapproximations for the dispersion relation in the long-wavelength limit in aweak-coupling regime.