Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: The Goldstone phonon and its Landau damping

TL;DR

This paper develops a microscopic density functional theory to describe the Goldstone phonon mode and its damping in a strongly interacting Fermi gas at finite temperature, matching experimental data without free parameters.

Contribution

It introduces a quantitative superfluid local density approximation for dynamic structure factors in strongly interacting Fermi gases, including phonon damping mechanisms.

Findings

Accurate prediction of the dynamic structure factor at low momentum.

Quantitative agreement with recent experimental measurements.

Temperature-dependent phonon damping rate calculations.

Abstract

We develop a microscopic theory of dynamic structure factor to describe the Bogoliubov-Anderson-Goldstone phonon mode and its damping rate in a strongly interacting Fermi gas at finite temperature. It is based on a density functional approach - the so-called superfluid local density approximation. The accuracy of the theory is quantitatively examined by comparing the theoretical predictions with the recent experimental measurements for the local dynamic structure factor of a nearly homogeneous unitary Fermi gas at low transferred momentum {[}S. Hoinka \textit{et al.}, Nat. Phys. \textbf{13}, 943 (2017){]}, without any free parameters. We calculate the dynamic structure factor as functions of temperature and transferred momentum, and determine the temperature evolution of the phonon damping rate, by considering the dominant decay process of the phonon mode via scatterings off fermionic quasiparticles. These predictions can be confronted with future Bragg scattering experiments on a unitary Fermi gas near the superfluid transition.