Bethe-Salpeter equations for 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 in superfluid Fermi gases within a moving optical lattice, revealing instabilities and comparing different theoretical approaches.

Contribution

It introduces a Bethe-Salpeter framework for superfluid Fermi gases in moving lattices and compares its predictions with other methods, highlighting agreement and differences.

Findings

BS equations accurately predict collective-mode dispersion

Superfluid state becomes unstable at high lattice velocities

Differences between methods grow with lattice velocity

Abstract

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.