Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: A two-fluid hydrodynamic description

TL;DR

This paper models the low-momentum dynamic structure factor of a strongly interacting Fermi gas using two-fluid hydrodynamics, revealing how sound damping varies near the superfluid transition and aiding the measurement of fundamental properties.

Contribution

It introduces a hydrodynamic framework to analyze sound damping and structure factors in a unitary Fermi gas, connecting experimental observations with superfluid properties.

Findings

Damping width of first sound increases near superfluid transition

Second sound may be observable close to the transition at certain momenta

Hydrodynamic theory applicability is estimated based on viscous relaxation time

Abstract

We provide a description of the dynamic structure factor of a homogeneous unitary Fermi gas at low momentum and low frequency, based on the dissipative two-fluid hydrodynamic theory. The viscous relaxation time is estimated and is used to determine the regime where the hydrodynamic theory is applicable and to understand the nature of sound waves in the density response near the superfluid phase transition. By collecting the best knowledge on the shear viscosity and thermal conductivity known so far, we calculate the various diffusion coefficients and obtain the damping width of the (first and second) sounds. We find that the damping width of the first sound is greatly enhanced across the superfluid transition and very close to the transition the second sound might be resolved in the density response for the transferred momentum up to the half of Fermi momentum. Our work is motivated by the recent measurement of the local dynamic structure factor at low momentum at Swinburne University of Technology and the on-going experiment on sound attenuation of a homogeneous unitary Fermi gas at Massachusetts Institute of Technology. We discuss how the measurement of the velocity and damping width of the sound modes in low-momentum dynamic structure factor may lead to an improved determination of the universal superfluid density, shear viscosity and thermal conductivity of a unitary Fermi gas.