Universal Quantum Viscosity in a Unitary Fermi Gas
Abstract
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 pT3/ħ2, where pT 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 T3/2 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.
Get full access to this article
View all available purchase options and get full access to this article.
Already a Subscriber?Sign In
Supplementary Material
References and Notes
1
O’Hara K. M., Hemmer S. L., Gehm M. E., Granade S. R., Thomas J. E., Observation of a strongly interacting degenerate Fermi gas of atoms. Science 298, 2179 (2002).
2
Giorgini S., Pitaevskii L. P., Stringari S., Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215 (2008).
3
Bloch I., Dalibard J., Zwerger W., Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885 (2008).
4
W. Ketterle, M. W. Zwierlein, “Making, probing and understanding ultracold Fermi gases,” in Ultracold Fermi Gases, Proceedings of the International School of Physics “Enrico Fermi,” Course CLXIV, Varenna, 20 to 30 June 2006 (IOS Press, Amsterdam, 2008).
5
Kinast J., et al., Heat capacity of a strongly interacting Fermi gas. Science 307, 1296 (2005).
6
Luo L., Clancy B., Joseph J., Kinast J., Thomas J. E., Measurement of the entropy and critical temperature of a strongly interacting Fermi gas. Phys. Rev. Lett. 98, 080402 (2007).
7
J. T. Stewart, J. P. Gaebler, C. A. Regal, D. S. Jin, Phys. Rev. Lett. (2006).
8
Hu H., Drummond P. D., Liu X.-J., Universal thermodynamics of strongly interacting Fermi gases. Nat. Phys. 3, 469 (2007).
9
Luo L., Thomas J. E., Thermodynamic measurements in a strongly interacting Fermi gas. J. Low Temp. Phys. 154, 1 (2009).
10
Horikoshi M., Nakajima S., Ueda M., Mukaiyama T., Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442 (2010).
11
Nascimbène S., Navon N., Jiang K. J., Chevy F., Salomon C., Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057 (2010).
12
Kovtun P. K., Son D. T., Starinets A. O., Viscosity in strongly interacting quantum field theories from black hole physics. Phys. Rev. Lett. 94, 111601 (2005).
13
Csernai L. P., Kapusta J. I., McLerran L. D., Strongly interacting low-viscosity matter created in relativistic nuclear collisions. Phys. Rev. Lett. 97, 152303 (2006).
14
Gelman B. A., Shuryak E. V., Zahed I., Ultracold strongly coupled gas: A near-ideal liquid. Phys. Rev. A 72, 043601 (2005).
15
Bruun G. M., Smith H., Shear viscosity and damping for a Fermi gas in the unitarity limit. Phys. Rev. A 75, 043612 (2007).
16
Schäfer T., Ratio of shear viscosity to entropy density for trapped fermions in the unitarity limit. Phys. Rev. A 76, 063618 (2007).
17
Turlapov A., et al., Is a gas of strongly interacting atomic fermions a nearly perfect fluid? J. Low Temp. Phys. 150, 567 (2008).
18
The experiments were performed far from p-wave Feshbach resonances. The relevant threshold energy for p-wave scattering was then comparable with the barrier height. Using the known C6 coefficients, the barrier height for 40K is 280 μK, whereas for 6Li the barrier height is 8 mK. Hence, for temperatures in the μK range as used in the experiments, p-wave scattering is negligible, and s-wave scattering dominates.
19
Kinast J., Turlapov A., Thomas J. E., Damping of a unitary Fermi gas. Phys. Rev. Lett. 94, 170404 (2005).
20
Materials and methods are available as supporting material on Science Online.
21
Son D. T., Vanishing bulk viscosities and conformal invariance of the unitary fermi gas. Phys. Rev. Lett. 98, 020604 (2007).
22
M. A. Escobedo, M. Mannarelli, C. Manuel, Bulk viscosities for cold Fermi superfluids close to the unitary limit. Phys Rev. A, http://arxiv.org/abs/0904.3023v2.
23
Ho T.-L., Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004).
24
Thomas J. E., Kinast J., Turlapov A., Virial theorem and universality in a unitary fermi gas. Phys. Rev. Lett. 95, 120402 (2005).
25
T. Schäfer, Dissipative fluid dynamics for the dilute Fermi gas at unitarity: Free expansion and rotation. http://arxiv.org/abs/1008.3876v1.
26
Menotti C., Pedri P., Stringari S., Expansion of an interacting fermi gas. Phys. Rev. Lett. 89, 250402 (2002).
27
Massignan P., Bruun G. M., Smith H., Viscous relaxation and collective oscillations in a trapped Fermi gas near the unitarity limit. Phys. Rev. A 71, 033607 (2005).
28
We give the damping rate 1/τ for a cylindrically symmetric cigar-shaped trap. For δ ≡ (ωx – ωy)/ << 1, with ωx,ωy the transverse trap frequencies, 1/τ contains an additional factor 1 – δ.
29
H. Guo, D. Wulin, C.-C. Chien, K. Levin, http://arxiv.org/abs/1008.0423v3.
30
Taylor E., Randeria M., Phys. Rev. A 81, 053610 (2010).
31
T. Enss, R. Haussmann, W. Zwerger, http://dx.doi.org/10.1016/j.aop.2010.10.002.
32
T. Scäfer, C. Chafin, Scaling flows and dissipation in the dilute Fermi gas at unitarity; http://arxiv.org/abs/0912.4236v3.
Information & Authors
Information
Published In
Science
Volume 331 • Issue 6013 • 7 January 2011
Pages: 58 - 61
History
Received: 16 July 2010
Accepted: 24 November 2010
9 December 2010
Copyright
Copyright © 2011, American Association for the Advancement of Science.
