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  Physics Express 2012, 2: 17
  Research Article
Collective-mode spectrum of a superfluid Fermi gas in a moving optical lattice: A Bethe-Salpeter approach
  Zlatko Koinova, Petar Koynovb  
a Department of Physics and Astronomy,University of Texas at San Antonio, San Antonio, TX 78249, USA
b Austin Community College, Austin, Texas, USA

  We derive the Bethe-Salpeter equations for the collective-mode spectrum of Fermi atoms of two hypefine states with a contact interaction loaded into a moving optical lattice. The collective excitation spectrum exhibits rotonlike minimum and the Landau instability takes place when the energy of the rotonlike minimum hits zero. Our approach is compared with the previous two approaches, namely the perturbation method and the Green’s function formalism. It is shown that the spectrum obtained by the Bethe-Salpeter equations is in an excellent agreement with corresponding spectrum obtained by the perturbation theory, while the Green’s function formalism provides slightly deferent results for the collective excitations.
  Optical lattice, Bethe-Salpeter, Landau instability  

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