Universal Quantum Viscosity in a Unitary Fermi Gas

TL;DR

The ratio of the shear viscosity to the entropy density is estimated and compared with that of a perfect fluid to compare with a string theory limit.

Abstract

A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, where the shear viscosity and other transport coefficients are universal functions of the density and temperature. At low temperatures, the viscosity has a universal quantum scale $\hbar n$ where $n$ is the density, while at high temperatures the natural scale is $p_T^3/\hbar^2$ where $p_T$ is the thermal momentum. We employ breathing mode damping to measure the shear viscosity at low temperature. At high temperature $T$, we employ anisotropic expansion of the cloud to find the viscosity, which exhibits precise $T^{3/2}$ scaling. In both experiments, universal hydrodynamic equations including friction and heating are used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare to that of a perfect fluid.

Figures (3)

• Figure 1: Anisotropic expansion. (A) Cloud absorption images for 0.2, 0 .3, 0.6, 0.9, 1.2 ms expansion time, $E=2.3\,E_F$; (B) Aspect ratio versus time. The expansion rate decreases at higher energy as the viscosity increases. Solid curves: Hydrodynamic theory with the viscosity as the fit parameter. Error bars denote statistical fluctuations in the aspect ratio.
• Figure 2: Trap averaged viscosity coefficient $\bar{\alpha}=\int d^3\mathbf{x}\,\eta/(\hbar N)$ versus initial energy per atom. Blue circles: Breathing mode measurements; Red squares: Anisotropic expansion measurements. Bars denote statistical error arising from the uncertainty in $E$ and the cloud dimensions. Inset: $\bar{\alpha}$ versus reduced temperature $\theta_0$ at the trap center prior to release of the cloud. The blue curve shows the fit $\alpha_0=\alpha_{3/2}\,\theta_0^{3/2}$, demonstrating the predicted universal high temperature scaling. Bars denote statistical error arising from the uncertainty in $\theta_0$ and $\bar{\alpha}$. A 3% systematic uncertainty in $E_F$ and 7% in $\theta_0$ arises from the systematic uncertainty in the absolute atom number SupportOnline.
• Figure 3: Estimated ratio of the shear viscosity to the entropy density. Blue circles: Breathing mode measurements; Red squares: Anisotropic expansion measurements; Inset: Red dashed line denotes the string theory limit. Bars denote statistical error arising from the uncertainty in $E$, $\bar{\alpha}$, and $S$SupportOnline.