Speed of sound in a superfluid Fermi gas in an optical lattice

TL;DR

This paper investigates the speed of sound in a superfluid Fermi gas of lithium-6 atoms within a 3D optical lattice, analyzing collective excitations on the BCS side of the Feshbach resonance.

Contribution

It provides a theoretical calculation of phonon dispersion and sound velocity in a superfluid Fermi gas using Bethe-Salpeter equations for the attractive Hubbard model.

Findings

Derived the phonon dispersion relation.

Calculated the speed of sound in the superfluid.

Analyzed effects of optical lattice on collective modes.

Abstract

A system of equal mixture of $^6Li$ atomic Fermi gas of two hyperfine states loaded into a cubic three-dimensional optical lattice is studied assuming a negative scattering length (BCS side of the Feshbach resonance). When the interaction is attractive, fermionic atoms can pair and form a superfluid. The dispersion of the phonon-like mode and the speed of sound in the long-wavelength limit are obtained by solving the Bethe-Salpeter equations for the collective modes of the attractive Hubbard Hamiltonian.