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arXiv:2402.14104 · Physical Review Research

Universal density shift coefficients for the thermal conductivity and shear viscosity of a unitary Fermi gas

Xiang Li, J. Huang, John E. Thomas

Published Oct 23, 2024• 6 citations
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Abstract

We measure universal temperature-independent density shifts for the thermal conductivity κ T and shear viscosity η , relative to the high temperature limits, for a normal phase unitary Fermi gas confined in a box potential. We show that a time-dependent kinetic theory model enables extraction of the hydrodynamic transport times τ η and τ κ from the time-dependent free decay of a spatially periodic density perturbation, yielding the static transport properties and density shifts, corrected for finite relaxation times. Published by the American Physical Society 2024

DOI
10.1103/physrevresearch.6.l042021

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We measure universal temperature-independent density shifts for the thermal conductivity κ T and shear viscosity η , relative to the high temperature limits, for a normal phase unitary Fermi gas confined in a box potential. We show that a time-dependent kinetic theory model enables extraction of the hydrodynamic transport times τ η and τ κ from the time-dependent free decay of a spatially periodic density perturbation, yielding the static transport properties and density shifts, corrected for finite relaxation times. Published by the American Physical Society 2024
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.
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.
We measure the free decay of a spatially periodic density profile in a normal fluid strongly interacting Fermi gas, which is confined in a box potential. This spatial profile is initially created in thermal equilibrium by a perturbing potential. After the perturbation is abruptly extinguished, the dominant spatial Fourier component exhibits an exponentially decaying (thermally diffusive) mode and a decaying oscillatory (first sound) mode, enabling independent measurement of the thermal conductivity and the shear viscosity directly from the time-dependent evolution.
Using the $\ensuremath{\varepsilon}$-expansion technique, we compute $\ensuremath{\eta}/s$, where $\ensuremath{\eta}$ is the shear viscosity and sss is the entropy density of the normal phase of unitary Fermi gas in $d=4\ensuremath{-}\ensuremath{\varepsilon}$ dimensions to leading order (LO) in $\ensuremath{\varepsilon}$. We use the kinetic theory approach and solve transport equations for a medium perturbed by a shear hydrodynamic flow. The collision integrals are calculated to ${\ensuremath{\varepsilon}}^{2}$, which is LO. The LO result is temperature independent with $\ensuremath{\eta}/s\ensuremath{\simeq}(0.11/{\ensuremath{\varepsilon}}^{2})(\ensuremath{\hbar}/{k}_{B})$. The d=3d=3d=3 prediction for $\ensuremath{\eta}/s$ exceeds the $\ensuremath{\hbar}/4\ensuremath{\pi}{k}_{B}$ bound by a factor of about 1.41.41.4.
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.
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.