The Shear Viscosity to Entropy Density Ratio of Trapped Fermions in the Unitarity Limit

TL;DR

Problem: determine $\eta/s$ in a strongly interacting unitary Fermi gas. Approach: combine Euler/hydrodynamic scaling with viscous corrections and thermodynamic inputs from Monte Carlo/calorimetry data, using local density approximation to relate global observables to $\eta/s$. Result: near the superfluid transition temperature, $\eta/s \approx 0.5\,\hbar/k_B$, indicating a very strongly correlated liquid and approaching the proposed lower bound more closely than most liquids. Significance: provides a cold-atom platform to test the universal $\eta/s$ bound $\ge \hbar/(4\pi k_B)$ and highlights universality with other strongly coupled systems such as the quark–gluon plasma.

Abstract

We extract the shear viscosity to entropy density ratio η/s of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature η/s is roughly equal to 1/2 in units of \hbar/k_B. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound 1/(4π) than any other known liquid.

Figures (2)

• Figure 1: Temperature dependence of the damping rate for the radial breathing mode of a trapped $^6$Li gas near the Feshbach resonance at 840 G, from Kinast et al. Kinast:2005. Here $\tau$ is the damping time and $\omega_\perp$ is the radial trap frequency. We have used the calibration curve in Kinast:2005b to convert the $\tilde{T}$ scale of Kinast:2005 to $T/T_F$.
• Figure 2: Viscosity to entropy density ratio of a cold atomic gas in the unitarity limit. This plot is based on the damping data published in Kinast:2005 and the thermodynamic data in Kinast:2005bLuo:2006. The dashed line shows the conjectured viscosity bound $\eta/s=1/(4\pi)$. The shaded band is a systematic error estimate based on the contribution to $\dot{E}$ from atoms outside a surface at optical depth one.