Anomalous Minimum in the Shear Viscosity of a Fermi Gas

We measure the static shear viscosity $\eta$ in a two-component Fermi gas near a broad collisional (Feshbach) resonance, as a function of interaction strength and energy. We find that $\eta$ has both a quadratic and a linear dependence on the interaction strength $1/(k_{FI}a)$, where $a$ is the $s$-wave scattering length and $k_{FI}$ is the Fermi wave vector for an ideal gas at the trap center. For energies above the superfluid transition, the minimum in $\eta$ as a function of interaction strength is significantly shifted toward the BEC side of resonance, to $1/(k_{FI}a)\simeq 0.25$.

Figure 1

Difference in shear viscosity on and off resonance, $\mathrm{\Delta }⟨{\alpha }_S⟩$, versus energy $\tilde{E}/E_F$ and interaction strength $1/(k_{FI}a)$. On the BEC side of resonance (left column), $1/(k_{FI}a)=$ (a) 0.83(6), (b) 0.55(5), and (c) 0.25(3). On the BCS side of resonance (right column) $1/(k_{FI}a)=$ (d) $-0.61(1)$, (e) $-0.34(1)$, and (f) $-0.16(3)$. Red line denotes linear fit to $\mathrm{\Delta }⟨{\alpha }_S⟩(\tilde{E})$. Dotted red lines show 1-$\sigma$ confidence interval. Blue (solid) lines show the resonant shear viscosity $⟨{\alpha }_S{⟩}_0$, (which denotes zero by construction).

Figure 2

Difference in shear viscosity on and off resonance, $\mathrm{\Delta }⟨{\alpha }_S⟩$, versus interaction strength $1/(k_{FI}a)$ at an energy of $\tilde{E}/E_F=1$. Black circles represent $\mathrm{\Delta }⟨{\alpha }_S⟩$ obtained from the linear fits in Fig. 1. Vertical error bars are the $1–\sigma$ confidence interval of the fits. The red (parabolic curve) is the best fit of ${\tilde{c}}_0+{\tilde{c}}_1/(k_{FI}a)+{\tilde{c}}_2/(k_{FI}a{)}^2$ to the data with ${\tilde{c}}_0=0.0$, ${\tilde{c}}_1=-1.7$, and ${\tilde{c}}_2=4.8$. From the fit, the minimum occurs at $1/(k_{F}a)=0.18$.

Figure 3

Off resonant shear viscosity coefficients $c_1$ and $c_2$ from Eq. (6), $⟨{\alpha }_S{⟩}_0+c_1{\mathrm{\Gamma }}_1^{1/3}(t)/(k_{FI}a)+c_2{\mathrm{\Gamma }}_1^{2/3}(t)/(k_{FI}a{)}^2$, obtained by integrating Eq. (5) and globally minimizing ${\chi }^2$ for aspect ratio data within a range of energies and interactions strengths. Red (upper) circles are $c_2$ versus energy. Blue (lower) circles are $c_1$ versus energy.