Sound propagation in elongated superfluid fermion clouds

TL;DR

This paper investigates sound propagation in elongated superfluid Fermi gases using hydrodynamic equations, analyzing the effects of trap geometry and density profiles across different interaction regimes, with predictions testable in experiments.

Contribution

It provides a theoretical analysis of sound speed in elongated superfluid Fermi gases, highlighting the impact of trap geometry and density profiles across BCS and unitary regimes.

Findings

Sound speed differs by a factor of sqrt(3/5) from homogeneous superfluids.

Radial density profile significantly influences sound propagation.

Predictions are experimentally testable with existing setups.

Abstract

We use hydrodynamic equations to study sound propagation in a superfluid Fermi gas inside a strongly elongated cigar-shaped trap, with main attention to the transition from the BCS to the unitary regime. We treat first the role of the radial density profile in the quasi-onedimensional limit 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 sqrt{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 set-up such as that exploited by M.R. Andrews et al. [Phys. Rev. Lett. 79, 553 (1997)] for an atomic Bose-Einstein condensate.