Sound propagation in elongated superfluid fermionic clouds

We use hydrodynamic equations to study sound propagation in a superfluid Fermi gas at zero temperature inside a strongly elongated cigar-shaped trap, with main attention to the transition from the BCS to the unitary regime. First, we treat the role of the radial density profile in the limit of a cylindrical geometry and then evaluate numerically the effect of the axial confinement in a configuration in which a hole is present in the gas density at the center of the trap. We find that in a strongly elongated trap the speed of sound in both the BCS and the unitary regime differs by a factor root 3/5 from that in a homogeneous three-dimensional superfluid. The predictions of the theory could be tested by measurements of sound-wave propagation in a setup such as that exploited by Andrews [Phys. Rev. Lett. 79, 553 (1997)] for an atomic Bose-Einstein condensate.