Dissipative superfluid hydrodynamics for the unitary Fermi gas

TL;DR

This paper constrains how the shear viscosity of a superfluid Fermi gas at unitarity depends on temperature, using experimental data and two-fluid hydrodynamics, revealing a significant decrease in viscosity in the superfluid phase.

Contribution

It provides a novel analysis of the temperature dependence of shear viscosity in a unitary Fermi gas using experimental aspect ratio measurements and two-fluid formalism.

Findings

Shear viscosity decreases significantly in the superfluid regime.

An exponential parametrization bounds shear viscosity at low temperatures.

Expansion experiments support a small velocity difference between normal and superfluid components.

Abstract

In this work we establish constraints on the temperature dependence of the shear viscosity $\eta$ in the superfluid phase of a dilute Fermi gas in the unitary limit. Our results are based on analyzing experiments that measure the aspect ratio of a deformed cloud after release from an optical trap. We discuss how to apply the two-fluid formalism to the unitary gas, and provide a suitable parametrization of the equation of state. We show that in expansion experiments the difference between the normal and superfluid velocities remains small, and can be treated as a perturbation. We find that expansion experiments favor a shear viscosity that decreases significantly in the superfluid regime. Using an exponential parametrization we find $\eta(T_c/(2T_F))< 0.37\eta (T_c/T_F)$, where $T_c$ is the critical temperature, $T_F$ is the local Fermi temperature of the gas.