Collective mode damping and viscosity in a 1D unitary Fermi gas

TL;DR

This paper analytically investigates the damping of collective modes in a 1D Fermi gas across the BCS-BEC crossover, revealing universal viscosity behavior at unitarity and linking damping to temperature measurement.

Contribution

It provides the first analytic derivation of viscosity and damping in a 1D Fermi gas across the entire BCS-BEC crossover using Bethe-Ansatz solutions.

Findings

Viscosity at unitarity is a universal constant, $oxed{0.38}$, in units of $oxed{ ext{hbar} imes n}$.

Damping of collective modes is highly sensitive to temperature, enabling precise thermometry in 1D Fermi gases.

Analytic expressions for viscosity are derived for the full crossover from weakly bound pairs to strongly bound dimers.

Abstract

We calculate the damping of the Bogoliubov-Anderson mode in a one-dimensional two-component attractive Fermi gas for arbitrary coupling strength within a quantum hydrodynamic approach. Using the Bethe-Ansatz solution of the 1D BCS-BEC crossover problem, we derive analytic results for the viscosity covering the full range from a Luther-Emery liquid of weakly bound pairs to a Lieb-Liniger gas of strongly bound bosonic dimers. At the unitarity point, the system is a Tonks-Girardeau gas with a universal constant $\alpha_{\zeta}=0.38$ in the viscosity $\zeta=\alpha_{\zeta}\hbar n$ for T=0. For the trapped case, we calculate the Q-factor of the breathing mode and show that the damping provides a sensitive measure of temperature in 1D Fermi gases.