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arXiv:1410.4835 · Physical Review Letters

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

J. A. Joseph, Ethan Elliott, John E. Thomas

Published Jul 6, 2015• 64 citations
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Abstract

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 α(S)(θ) versus reduced temperature θ from the cloud-averaged measurements ⟨α(S)⟩, and compare α(S) to several microscopic theories. We find that α(S) reveals features that were previously hidden in ⟨α(S)⟩.

DOI
10.1103/physrevlett.115.020401

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•Jul 30, 2010•4 citations
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 α(S)(θ) versus reduced temperature θ from the cloud-averaged measurements ⟨α(S)⟩, and compare α(S) to several microscopic theories. We find that α(S) reveals features that were previously hidden in ⟨α(S)⟩.
We determine the shear viscosity of the ultracold Fermi gas at unitarity in the normal phase using hydrodynamic expansion data. The analysis is based on a generalized fluid dynamic framework which ensures a smooth transition between the fluid dynamic core of the cloud and the ballistic corona. We use expansion data taken by Joseph, Elliott, and Thomas [Shear Viscosity of a Universal Fermi Gas Near the Superfluid Phase Transition, Phys. Rev. Lett. 115, 020401 (2015).PRLTAO0031-900710.1103/PhysRevLett.115.020401] and measurements of the equation of state by Ku et al. [Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).SCIEAS0036-807510.1126/science.1214987]. We find that the shear viscosity to particle density ratio just above the critical temperature is η/n|_{T_{c}}=0.41±0.11. We also obtain evidence that the shear viscosity to entropy density ratio has a minimum slightly above T_{c} with η/s|_{min}=0.50±0.10.
Recent experiments on the shear viscosity η in a unitary Fermi gas fail to see the theoretically predicted upturn in η at the lower T. In this Letter, we compute η in a fashion which is demonstrably consistent with conservation laws and, in the process, provide an understanding of recent experiments. We show that this disagreement with prior theories cannot be readily attributed to the trap, since (via edge effects) trap-averaged viscosities will be larger than their homogeneous counterparts. The small values of η we find can be simply understood; they reflect the fact that the Goldstone bosons (phonons) do not couple to transverse probes such as η, and fermionic excitations, which determine the viscosity, are necessarily absent in the ground state.
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 ℏ n 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.
A Fermi gas of atoms with resonant interactions is predicted to obey universal hydrodynamics, in which 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 ħ n, where n is the density and ħ is Planck's constant h divided by 2π, whereas at high temperatures the natural scale is p(T)(3)/ħ(2), where p(T) is the thermal momentum. We used breathing mode damping to measure the shear viscosity at low temperature. At high temperature T, we used 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 were used to extract the viscosity. We estimate the ratio of the shear viscosity to the entropy density and compare it with that of a perfect fluid.
We present an ab initio determination of the shear viscosity $\ensuremath{\eta}$ of the unitary Fermi gas, based on finite temperature quantum Monte Carlo calculations and the Kubo linear-response formalism. We determine the temperature dependence of the shear viscosity-to-entropy density ratio $\ensuremath{\eta}/s$. The minimum of $\ensuremath{\eta}/s$ appears to be located above the critical temperature for the superfluid-to-normal phase transition with the most probable value being $(\ensuremath{\eta}/s{)}_{\mathrm{min}}\ensuremath{\approx}0.2\ensuremath{\hbar}/{k}_{B}$, which is close the Kovtun-Son-Starinets universal value $\ensuremath{\hbar}/(4\ensuremath{\pi}{k}_{B})$.
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 ℏn\hbar nℏn where nnn is the density, while at high temperatures the natural scale is pT3/ℏ2p_T^3/\hbar^2pT3​/ℏ2 where pTp_TpT​ is the thermal momentum. We employ breathing mode damping to measure the shear viscosity at low temperature. At high temperature TTT, we employ anisotropic expansion of the cloud to find the viscosity, which exhibits precise T3/2T^{3/2}T3/2 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.