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Bulletin of the American Physical Society

Calculation of collective modes of atoms in an optical lattice

Sara Bergkvist, Emil Lundh, Patrik Henelius, Anders Rosengren

Published Mar 23, 2005• 0 citations
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We have derived the Bethe-Salpeter (BS) equations for the collective-mode spectrum of a mixture of fermion atoms of two hyperfine states 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. The BS approach is compared with the other existing methods for calculating the collective-mode spectrum. In particular, it is shown that the spectrum obtained by the BS equations in an excellent agreement with corresponding spectrum obtained by the perturbation theory, while the Green's function formalism provides slightly different results for the collective excitations.
We derive the Bethe-Salpeter (BS) equations for the collective-mode spectrum of superfluid Fermi gases of equal mixture of atomic Fermi gas of two hyperfine states loaded into a moving optical lattice. In a moving lattice the superfluid state is unstable due to spontaneous emission of the short-wavelength rotonlike excitations which appear in the spectrum of the collective modes. It is shown that the spectrum obtained by the BS equations is in an excellent agreement with the collective-mode dispersion calculated by the perturbation approach, while there are some differences between the results obtained by density response function method and by the BS approach. The difference increases with increasing the lattice velocity, which can be seen in the analytical approximations for the dispersion relation in the long-wavelength limit in a weak-coupling regime.