Abstract
We measure the shear viscosity in a two-component Fermi gas of atoms, tuned to a broad s-wave collisional (Feshbach) resonance. At resonance, the atoms strongly interact and exhibit universal behavior, where the equilibrium thermodynamic properties and transport coefficients are universal functions of density n and temperature T. We present a new calibration of the temperature as a function of global energy, which is directly measured from the cloud profiles. Using the calibration, the trap-averaged shear viscosity in units of ℏn is determined as a function of the reduced temperature at the trap center, from nearly the ground state to the unitary two-body regime. Low-temperature data are obtained from the damping rate of the radial breathing mode, whereas high-temperature data are obtained from hydrodynamic expansion measurements. We also show that the best fit to the high-temperature expansion data is obtained for a vanishing bulk viscosity. The measured trap-averaged entropy per particle and shear viscosity are used to estimate the ratio of shear viscosity to entropy density, which is compared with that conjectured for a perfect fluid.
Highlights
The measurement of the shear viscosity is currently of particular interest in the context of a recent conjecture, derived using string theory methods, which defines a perfect normal fluid [1]
The perfect fluid conjecture states that the ratio of the shear viscosity η to the entropy density s has a universal minimum, η s
The bulk viscosity is predicted to vanish in the normal fluid phase at unitarity [26, 27], which is why we did not include the bulk viscosity in our initial analysis to extract the shear viscosity
Summary
The measurement of the shear viscosity is currently of particular interest in the context of a recent conjecture, derived using string theory methods, which defines a perfect normal fluid [1]. The perfect fluid conjecture states that the ratio of the shear viscosity η to the entropy density s has a universal minimum, η s. To obtain strong interactions, characterized by a divergent s-wave scattering length [8], a bias magnetic field is used to tune the gas to a broad collisional (Feshbach) resonance, where the range of the collision potential is small compared to the interparticle spacing. In this so-called unitary regime, the two-body interaction potential produces no relevant length scales. For much higher temperatures above the Fermi temperature, one expects that l ≃ λT ∝ hT −1/2, so that the shear viscosity scales as η ∝ h/λ3T ∝ T 3/2/h2
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