Sound propagation and oscillations of a superfluid Fermi gas in the presence of a one-dimensional optical lattice

We develop the hydrodynamic theory of Fermi superfluids in the presence of a periodic potential. The relevant parameters governing the propagation of sound (compressibility and effective mass) are calculated in the weakly interacting BCS limit. The conditions of stability of the superfluid motion with respect to creation of elementary excitations are discussed. We also evaluate the frequency of the center-of-mass oscillation when the superfluid gas is additionally confined by a harmonic trap.

Figure 1

Function $f$ [see Eq. (23)] versus the parameter $y={ϵ}_F∕2\delta$ (solid line). The asymptotic limit $5∕8y$ is also shown (dashed line).