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

TL;DR

This paper derives Bethe-Salpeter equations to analyze the collective excitations of a superfluid Fermi gas in a moving optical lattice, revealing roton-like minima and instabilities, and compares this approach with other methods.

Contribution

It introduces a Bethe-Salpeter framework for calculating the collective-mode spectrum of superfluid Fermi gases in optical lattices, showing its agreement with perturbation theory.

Findings

Bethe-Salpeter equations accurately predict collective excitations.

Roton-like minima appear in the excitation spectrum.

Landau instability occurs at the roton minimum energy zero.

Abstract

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.