First and second sound in a strongly interacting Fermi gas

TL;DR

This paper investigates first and second sound modes in a strongly interacting Fermi gas at unitarity using a variational approach, revealing similarities to superfluid helium and conditions for hybridization and observation of second sound.

Contribution

It provides a detailed analysis of two-fluid hydrodynamics in Fermi gases, highlighting the behavior of sound modes in uniform and trapped conditions, and proposes methods to observe second sound.

Findings

First and second sound modes resemble those in superfluid helium.

Degeneracy and hybridization of sound modes occur at specific temperatures in traps.

Second sound can be excited via local heat perturbations.

Abstract

Using a variational approach, we solve the equations of two-fluid hydrodynamics for a uniform and trapped Fermi gas at unitarity. In the uniform case, we find that the first and second sound modes are remarkably similar to those in superfluid Helium, a consequence of strong interactions. In the presence of harmonic trapping, first and second sound become degenerate at certain temperatures. At these points, second sound hybridizes with first sound and is strongly coupled with density fluctuations, giving a promising way of observing second sound. We also discuss the possibility of exciting second sound by generating local heat perturbations.