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  • Letter
  • Open Access

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

Xiang Li, J. Huang, and J. E. Thomas*

  • *Contact author: jethoma7@ncsu.edu

Phys. Rev. Research 6, L042021 – Published 23 October, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L042021

Abstract

We measure universal temperature-independent density shifts for the thermal conductivity κT 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 τη and τκ 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.

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References (35)

  1. A. Adams, L. D. Carr, T. Schäfer, P. Steinberg, and J. E. Thomas, Strongly correlated quantum fluids: Ultracold quantum gases, quantum chromodynamic plasmas and holographic duality, New J. Phys. 14, 115009 (2012).
  2. I. Bloch, J. Dalibard, and S. Nascimbène, Quantum simulations with ultracold quantum gases, Nat. Phys. 8, 267 (2012).
  3. G. C. Strinati, P. Pieri, G. Röpke, P. Schuck, and M. Urban, The BCS-BEC crossover: From ultra-cold Fermi gases to nuclear systems, Phys. Rep. 738, 1 (2018).
  4. G. M. Bruun and H. Smith, Shear viscosity and damping for a Fermi gas in the unitary limit, Phys. Rev. A 75, 043612 (2007).
  5. E. Taylor and M. Randeria, Viscosity of strongly interacting quantum fluids: Spectral functions and sum rules, Phys. Rev. A 81, 053610 (2010).
  6. M. Braby, J. Chao, and T. Schäfer, Thermal conductivity and sound attenuation in dilute atomic Fermi gases, Phys. Rev. A 82, 033619 (2010).
  7. M. Braby, J. Chao, and T. Schäfer, Viscosity spectral functions of the dilute Fermi gas in kinetic theory, New J. Phys. 13, 035014 (2011).
  8. T. Enss, R. Haussmann, and W. Zwerger, Viscosity and scale invariance in the unitary Fermi gas, Ann. Phys. 326, 770 (2011).
  9. H. Guo, D. Wulin, C.-C. Chien, and K. Levin, Microscopic approach to shear viscosities of unitary Fermi gases above and below the superfluid transition, Phys. Rev. Lett. 107, 020403 (2011).
  10. G. Wlazłowski, P. Magierski, and J. E. Drut, Shear viscosity of a unitary Fermi gas, Phys. Rev. Lett. 109, 020406 (2012).
  11. P. Romatschke and R. E. Young, Implications of hydrodynamic fluctuations for the minimum shear viscosity of the dilute Fermi gas at unitarity, Phys. Rev. A 87, 053606 (2013).
  12. M. Bluhm, J. Hou, and T. Schäfer, Determination of the density and temperature dependence of the shear viscosity of a unitary Fermi gas based on hydrodynamic flow, Phys. Rev. Lett. 119, 065302 (2017).
  13. B. Frank, W. Zwerger, and T. Enss, Quantum critical thermal transport in the unitary Fermi gas, Phys. Rev. Res. 2, 023301 (2020).
  14. J. Hofmann, High-temperature expansion of the viscosity in interacting quantum gases, Phys. Rev. A 101, 013620 (2020).
  15. H. Zhou and Y. Ma, Thermal conductivity of an ultracold Fermi gas in the BCS-BEC crossover, Sci. Rep. 11, 1228 (2021).
  16. K. M. O'Hara, S. L. Hemmer, M. E. Gehm, S. R. Granade, and J. E. Thomas, Observation of a strongly interacting degenerate Fermi gas of atoms, Science 298, 2179 (2002).
  17. T.-L. Ho, Universal thermodynamics of degenerate quantum gases in the unitarity limit, Phys. Rev. Lett. 92, 090402 (2004).
  18. C. Cao, E. Elliott, J. Joseph, H. Wu, J. Petricka, T. Schäfer, and J. E. Thomas, Universal quantum viscosity in a unitary Fermi gas, Science 331, 58 (2011).
  19. J. A. Joseph, E. Elliott, and J. E. Thomas, Shear viscosity of a unitary Fermi gas near the superfluid phase transition, Phys. Rev. Lett. 115, 020401 (2015).
  20. N. Navon, R. P. Smith, and Z. Hadzibabic, Quantum gases in optical boxes, Nat. Phys. 17, 1334 (2021).
  21. L. Baird, X. Wang, S. Roof, and J. E. Thomas, Measuring the hydrodynamic linear response of a unitary Fermi gas, Phys. Rev. Lett. 123, 160402 (2019).
  22. P. B. Patel, Z. Yan, B. Mukherjee, R. J. Fletcher, J. Struck, and M. W. Zwierlein, Universal sound diffusion in a strongly interacting Fermi gas, Science 370, 1222 (2020).
  23. X. Wang, X. Li, I. Arakelyan, and J. E. Thomas, Hydrodynamic relaxation in a strongly interacting Fermi gas, Phys. Rev. Lett. 128, 090402 (2022).
  24. X. Li, X. Luo, S. Wang, K. Xie, X.-P. Liu, H. Hu, Y.-A. Chen, X.-C. Yao, and J.-W. Pan, Second sound attenuation near quantum criticality, Science 375, 528 (2022).
  25. H. Hu, P. Zou, and X.-J. Liu, Low-momentum dynamic structure factor of a strongly interacting Fermi gas at finite temperature: A two-fluid hydrodynamic description, Phys. Rev. A 97, 023615 (2018).
  26. Z. Yan, P. B. Patel, B. Mukherjee, C. J. Vale, R. J. Fletcher, and M. W. Zwierlein, Thermography of the superfluid transition in a strongly interacting Fermi gas, Science 383, 629 (2024).
  27. D. T. Son, Vanishing bulk viscosities and conformal invariance of the unitary Fermi gas, Phys. Rev. Lett. 98, 020604 (2007).
  28. Y.-H. Hou, L. P. Pitaevskii, and S. Stringari, Scaling solutions of the two-fluid hydrodynamic equations in a harmonically trapped gas at unitarity, Phys. Rev. A 87, 033620 (2013).
  29. E. Elliott, J. A. Joseph, and J. E. Thomas, Observation of conformal symmetry breaking and scale invariance in expanding Fermi gases, Phys. Rev. Lett. 112, 040405 (2014).
  30. M. Ku, A. T. Sommer, L. W. Cheuk, and M. W. Zwierlein, Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas, Science 335, 563 (2012).
  31. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L042021 for discussion of the linearized hydrodynamic equations, the kinetic theory relaxation model, and the determination of the static transport properties.
  32. In a simple Drude model with a transport time τ, the electrical conductivity is σ(ω)=σ(0)/(1−iωτ).
  33. Note that the Fermi time defined in Ref. [8], Fig. 6 is ℏ/εF, which is a factor of π smaller than λF/vF.
  34. The vertical error bars in Figs. 3 and 4 denote ±2εii, where εij is the error matrix obtained from χ2(τη,τκ) with A and cT fixed.
  35. L. D. Landau and E. M. Lifshitz, Fluid Dynamics, Course of Theoretical Physics Vol. VI (Pergamon Press, Oxford, 1959)

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