First and second sound in a highly elongated Fermi gas at unitarity

TL;DR

This paper models first and second sound propagation in a highly elongated unitary Fermi gas at finite temperature, providing theoretical predictions that align with recent experimental observations.

Contribution

It presents a detailed hydrodynamic analysis of sound modes in a unitary Fermi gas, including superfluid effects and thermodynamic functions, with explicit calculations of sound velocities.

Findings

Both first and second sound modes are calculated as functions of temperature.

Density fluctuations in second sound are large enough for experimental detection.

Theoretical results are compared with recent experimental data.

Abstract

We consider a Fermi gas at unitarity trapped by a highly elongated harmonic potential and solve the equations of two fluid hydrodynamics at finite temperature. The propagation of sound waves as well as the discretized solutions in the presence of weak axial trapping are considered. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both first sound and second sound solutions are calculated as a function of temperature and the role of the superfluid density is explicitly pointed out. The density fluctuations in the second sound wave are found to be large enough to be measured as a consequence of the finite thermal expansion coefficient of the gas. Emphasis is given to the comparison with recent experimental data.