Shear Viscosity of a Unitary Fermi Gas Near the Superfluid Phase Transition

We measure the shear viscosity for a resonantly interacting Fermi gas as a function of temperature from nearly the ground state through the superfluid phase transition into the high temperature regime. Further, we demonstrate an iterative method to estimate the local shear viscosity coefficient ${\alpha }_S(\theta )$ versus reduced temperature $\theta$ from the cloud-averaged measurements $⟨{\alpha }_S⟩$, and compare ${\alpha }_S$ to several microscopic theories. We find that ${\alpha }_S$ reveals features that were previously hidden in $⟨{\alpha }_S⟩$.

Figure 1

Trap-averaged shear viscosity coefficient $⟨{\alpha }_S⟩$, where the shear viscosity is $\eta ={\alpha }_S\hslash n$. The solid blue points show the $⟨{\alpha }_S⟩$ data versus reduced temperature ${\theta }_0$ at the trap center, after binning the raw data (inset) in ${\theta }_0$. The vertical dashed line denotes the critical temperature at the trap center ${\theta }_c=0.167(13)$ [18]. The red solid line is obtained by integrating ${\alpha }_S(\theta )$, which is estimated from the $⟨{\alpha }_S⟩$ data using an image processing algorithm.

Figure 2

Local shear viscosity coefficient ${\alpha }_S$ (blue dots) versus reduced temperature $\theta =T/T_F(n)$. The prediction from the two-body Boltzmann equation [12] $2.77{\theta }^{3/2}$ (black curve) is used as a seed function to initialize the iteration procedure and as a constraint at large $\theta$.

Figure 3

Extracted local shear viscosity coefficient ${\alpha }_S$ (blue dots) versus reduced temperature $\theta =T/T_F(n)$ near the superfluid transition temperature, where the local shear viscosity is $\eta ={\alpha }_S(\theta )\hslash n$. The vertical dashed line denotes the critical temperature ${\theta }_c=0.167(13)$ [18]. Blue bands denote the standard error corresponding to the statistical uncertainty in $⟨{\alpha }_S⟩$; Red solid line from Guo et al., Ref. [4]; Green dotted curve from Enss et al., Ref. [15]; Purple dot-dashed curve from Wlazlowski et al., Ref. [16]; Black-solid line prediction from kinetic theory ${\alpha }_S=2.77{\theta }^{3/2}$ [12].

Figure 4

Slope of the shear viscosity coefficient ${\alpha }_S$ versus reduced temperature $\theta$, showing a peak at $T_c$. The vertical dashed line denotes the critical reduced temperature.

Figure 5

Ratio of shear viscosity $\eta$ to the entropy density $s$, in units of $\hslash /k_B$, versus reduced temperature $\theta =T/T_F(n)$. Blue dots are the ratio of the local shear viscosity, obtained from our matrix inversion method, to the entropy density measured in Ref. [18]. Blue bands denote the standard error for quadratically combining the statistical uncertainties in $⟨{\alpha }_S⟩$ and in $s$. The vertical dashed line denotes the critical reduced temperature and the horizontal dashed line at $1/(4\pi )$ indicates the KSS lower bound [1].