Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Letter
  • Published:

Second sound and the superfluid fraction in a Fermi gas with resonant interactions

Nature volume 498, pages 78–81 (2013)Cite this article

Subjects

Abstract

Superfluidity is a macroscopic quantum phenomenon occurring in systems as diverse as liquid helium and neutron stars. It occurs below a critical temperature1,2 and leads to peculiar behaviour such as frictionless flow, the formation of quantized vortices and quenching of the moment of inertia. Ultracold atomic gases offer control of interactions and external confinement, providing unique opportunities to explore superfluid phenomena. Many such (finite-temperature) phenomena can be explained in terms of a two-fluid mixture3,4 comprising a normal component, which behaves like an ordinary fluid, and a superfluid component with zero viscosity and zero entropy. The two-component nature of a superfluid is manifest in ‘second sound’, an entropy wave in which the superfluid and the non-superfluid components oscillate with opposite phases (as opposed to ordinary ‘first sound’, where they oscillate in phase). Here we report the observation of second sound in an ultracold Fermi gas with resonant interactions. The speed of second sound depends explicitly on the value of the superfluid fraction5, a quantity that is sensitive to the spectrum of elementary excitations6. Our measurements allow us to extract the temperature dependence of the superfluid fraction, a previously inaccessible quantity that will provide a benchmark for theories of strongly interacting quantum gases.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Observing the propagation of first and second sound.
Figure 2: Extracting the sound speeds.
Figure 3: Normalized sound speeds and the 1D superfluid fraction.
Figure 4: Superfluid fraction for the homogeneous case.

Similar content being viewed by others

References

  1. Kapitza, P. Viscosity of liquid helium below the λ-point. Nature 141, 74 (1938)

    Article  ADS  CAS  Google Scholar 

  2. Allen, J. F. & Misener, A. D. Flow phenomena in liquid helium II. Nature 142, 643–644 (1938)

    Article  ADS  CAS  Google Scholar 

  3. Tisza, L. Transport phenomena in helium II. Nature 141, 913 (1938)

    Article  ADS  CAS  Google Scholar 

  4. Landau, L. The theory of superfluidity of helium II. J. Phys. (Mosc.) 5, 71–90 (1941)

    CAS  MATH  Google Scholar 

  5. Khalatnikov, I. M. An Introduction to the Theory of Superfluidity (Benjamin, 1965)

    Google Scholar 

  6. Landau, L. On the theory of superfluidity of helium II. J. Phys. (Mosc.) 11, 91–92 (1947)

    CAS  Google Scholar 

  7. Atkins, K. R. Liquid helium (Cambridge Univ. Press, 1959)

    MATH  Google Scholar 

  8. Peshkov, V. P. “Second sound” in helium II. J. Phys. (Mosc.) 8, 381 (1944)

    CAS  Google Scholar 

  9. Meppelink, R., Koller, S. B. & van der Straten, P. Sound propagation in a Bose-Einstein condensate at finite temperatures. Phys. Rev. A 80, 043605 (2009)

    Article  ADS  Google Scholar 

  10. Stamper-Kurn, D. M., Miesner, H.-J., Inouye, S., Andrews, M. R. & Ketterle, W. Collisionless and hydrodynamic excitations of a Bose-Einstein condensate. Phys. Rev. Lett. 81, 500–503 (1998)

    Article  ADS  CAS  Google Scholar 

  11. Meppelink, R., Koller, S. B., Vogels, J. M., Stoof, H. T. C. & van der Straten, P. Damping of superfluid flow by a thermal cloud. Phys. Rev. Lett. 103, 265301 (2009)

    Article  ADS  CAS  Google Scholar 

  12. Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008)

    Article  ADS  CAS  Google Scholar 

  13. Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

    Article  ADS  CAS  Google Scholar 

  14. Ho, T.-L. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004)

    Article  ADS  Google Scholar 

  15. Kinast, J. et al. Heat capacity of a strongly interacting Fermi gas. Science 307, 1296–1299 (2005)

    Article  ADS  CAS  Google Scholar 

  16. Horikoshi, M., Nakajima, S., Ueda, M. & Mukaiyama, T. Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442–445 (2010)

    Article  ADS  CAS  Google Scholar 

  17. Nascimbène, S., Navon, N., Jiang, K. J., Chevy, F. & Salomon, C. Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057–1060 (2010)

    Article  ADS  Google Scholar 

  18. Ku, M. J. H., Sommer, A. T., Cheuk, L. W. & Zwierlein, M. W. Revealing the superfluid lambda transition in the universal thermodynamics of a unitary Fermi gas. Science 335, 563–567 (2012)

    Article  ADS  CAS  Google Scholar 

  19. Tey, M. K. et al. Collective modes in a unitary Fermi gas across the superfluid phase transition. Phys. Rev. Lett. 110, 055303 (2013)

    Article  ADS  Google Scholar 

  20. Andrews, M. R. et al. Propagation of sound in a Bose-Einstein condensate. Phys. Rev. Lett. 79, 553–556 (1997)

    Article  ADS  CAS  Google Scholar 

  21. Joseph, J. et al. Measurement of sound velocity in a Fermi gas near a Feshbach resonance. Phys. Rev. Lett. 98, 170401 (2007)

    Article  ADS  Google Scholar 

  22. Arahata, E. & Nikuni, T. Propagation of second sound in a superfluid Fermi gas in the unitary limit. Phys. Rev. A 80, 043613 (2009)

    Article  ADS  Google Scholar 

  23. Hu, H., Taylor, E., Liu, X.-J., Stringari, S. & Griffin, A. Second sound and the density response function in uniform superfluid atomic gases. N. J. Phys. 12, 043040 (2010)

    Article  Google Scholar 

  24. Bertaina, G., Pitaevskii, L. & Stringari, S. First and second sound in cylindrically trapped gases. Phys. Rev. Lett. 105, 150402 (2010)

    Article  ADS  CAS  Google Scholar 

  25. Hou, Y.-H., Pitaevskii, L. & Stringari, S. First and second sound in a highly elongated Fermi gas at unitarity. Preprint at http://arxiv.org/abs/1301.4419 (2013)

  26. Dash, J. G. & Taylor, R. D. Hydrodynamics of oscillating disks in viscous fluids: Density and viscosity of normal fluid in pure He4 from 1.2°K to the lambda point. Phys. Rev. 105, 7–24 (1957)

    Article  ADS  CAS  Google Scholar 

  27. Heiselberg, H. Sound modes at the BCS-BEC crossover. Phys. Rev. A 73, 013607 (2006)

    Article  ADS  Google Scholar 

  28. Nascimbène, S. et al. Collective oscillations of an imbalanced Fermi gas: axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402 (2009)

    Article  ADS  Google Scholar 

  29. Sommer, A., Ku, M., Roati, G. & Zwierlein, M. W. Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201–204 (2011)

    Article  ADS  CAS  Google Scholar 

  30. Stadler, D., Krinner, S., Meineke, J., Brantut, J.-P. & Esslinger, T. Observing the drop of resistance in the flow of a superfluid Fermi gas. Nature 491, 736–739 (2012)

    Article  ADS  CAS  Google Scholar 

  31. Jochim, S. et al. Bose-Einstein condensation of molecules. Science 302, 2101–2103 (2003)

    Article  ADS  CAS  Google Scholar 

Download references

Acknowledgements

We thank E. R. Sánchez Guajardo for his contributions in the early stage of this work, and P. van der Straten for discussions. The Innsbruck team acknowledges support from the Austrian Science Fund (FWF) within SFB FoQuS (project no. F4004-N16). The Trento team acknowledges support from the European Research Council through the project QGBE and from the Provincia Autonoma di Trento. We dedicate the present work to our late friend and colleague A. Griffin, who enthusiastically promoted the idea of measuring second sound in Fermi gases.

Author information

Authors and Affiliations

  1. Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria,

    Leonid A. Sidorenkov, Meng Khoon Tey & Rudolf Grimm

  2. Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria,

    Leonid A. Sidorenkov, Meng Khoon Tey & Rudolf Grimm

  3. Dipartimento di Fisica, Universitá di Trento and INO-CNR BEC Center, I-38123 Povo, Italy,

    Yan-Hua Hou, Lev Pitaevskii & Sandro Stringari

  4. Kapitza Institute for Physical Problems, Russian Academy of Sciences, 119334 Moscow, Russia,

    Lev Pitaevskii

Authors
  1. Leonid A. Sidorenkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Meng Khoon Tey
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rudolf Grimm
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yan-Hua Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lev Pitaevskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Sandro Stringari
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

L.A.S. and M.K.T. equally contributed to the experimental work and the data analysis under the supervision of R.G. The new experimental methods were conceived by these three authors jointly. The theoretical work was performed by Y.-H.H., L.P. and S.S.

Corresponding author

Correspondence to Meng Khoon Tey.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

This file contains Supplementary Text and Data, Supplementary Figures 1-3 and Supplementary References. (PDF 195 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sidorenkov, L., Tey, M., Grimm, R. et al. Second sound and the superfluid fraction in a Fermi gas with resonant interactions. Nature 498, 78–81 (2013). https://doi.org/10.1038/nature12136

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature12136

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing