Second sound and the density response function in uniform superfluid atomic gases

The equations of fluid dynamics of normal fluids are modified when one is dealing with a superfluid. The equations of two-fluid hydrodynamics were formulated by Landau in 1941 for superfluid Helium. They predict the existence of first and second sound oscillations. The Landau equations also describe superfluid gases and are quite different from the usual mean-field Gross-Pitaevskii equations. To access two-fluid hydrodynamics in trapped ultracold gases , one needs strong interactions (short collision times). This strong-interaction regime can be reached in Fermi gases by using a Feshbach resonance to make the s-wave scattering length very large. This has renewed interested in observing second sound in superfluid quantum gases. We have calculated the temperature dependence of the velocity and amplitude of the first and second sound resonances in the density response function of a uniform strongly interacting Fermi superfluid in the two-fluid region. Contrary to expectations based on superfluid Helium, the amplitude of first and second sound are comparable in the dynamic structure factor of Fermi gases near unitarity at temperatures well below the superfluid transition temperature. This agrees with and clarifies recent predictions by Arahata and Nikuni on density pulse propagation in such gases. Our calculations shows that two-fluid hydrodynamics can be studied easily in strongly interacting superfluid Fermi gases using density probes. In particular, second sound should be clearly visible as a density pulse in propagation experiments in cigar-shaped traps over a wide range of temperatures.