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.
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Kapitza, P. Viscosity of liquid helium below the λ-point. Nature 141, 74 (1938)
Allen, J. F. & Misener, A. D. Flow phenomena in liquid helium II. Nature 142, 643–644 (1938)
Tisza, L. Transport phenomena in helium II. Nature 141, 913 (1938)
Landau, L. The theory of superfluidity of helium II. J. Phys. (Mosc.) 5, 71–90 (1941)
Khalatnikov, I. M. An Introduction to the Theory of Superfluidity (Benjamin, 1965)
Landau, L. On the theory of superfluidity of helium II. J. Phys. (Mosc.) 11, 91–92 (1947)
Atkins, K. R. Liquid helium (Cambridge Univ. Press, 1959)
Peshkov, V. P. “Second sound” in helium II. J. Phys. (Mosc.) 8, 381 (1944)
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)
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)
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)
Giorgini, S., Pitaevskii, L. P. & Stringari, S. Theory of ultracold atomic Fermi gases. Rev. Mod. Phys. 80, 1215–1274 (2008)
Bloch, I., Dalibard, J. & Zwerger, W. Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)
Ho, T.-L. Universal thermodynamics of degenerate quantum gases in the unitarity limit. Phys. Rev. Lett. 92, 090402 (2004)
Kinast, J. et al. Heat capacity of a strongly interacting Fermi gas. Science 307, 1296–1299 (2005)
Horikoshi, M., Nakajima, S., Ueda, M. & Mukaiyama, T. Measurement of universal thermodynamic functions for a unitary Fermi gas. Science 327, 442–445 (2010)
Nascimbène, S., Navon, N., Jiang, K. J., Chevy, F. & Salomon, C. Exploring the thermodynamics of a universal Fermi gas. Nature 463, 1057–1060 (2010)
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)
Tey, M. K. et al. Collective modes in a unitary Fermi gas across the superfluid phase transition. Phys. Rev. Lett. 110, 055303 (2013)
Andrews, M. R. et al. Propagation of sound in a Bose-Einstein condensate. Phys. Rev. Lett. 79, 553–556 (1997)
Joseph, J. et al. Measurement of sound velocity in a Fermi gas near a Feshbach resonance. Phys. Rev. Lett. 98, 170401 (2007)
Arahata, E. & Nikuni, T. Propagation of second sound in a superfluid Fermi gas in the unitary limit. Phys. Rev. A 80, 043613 (2009)
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)
Bertaina, G., Pitaevskii, L. & Stringari, S. First and second sound in cylindrically trapped gases. Phys. Rev. Lett. 105, 150402 (2010)
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)
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)
Heiselberg, H. Sound modes at the BCS-BEC crossover. Phys. Rev. A 73, 013607 (2006)
Nascimbène, S. et al. Collective oscillations of an imbalanced Fermi gas: axial compression modes and polaron effective mass. Phys. Rev. Lett. 103, 170402 (2009)
Sommer, A., Ku, M., Roati, G. & Zwierlein, M. W. Universal spin transport in a strongly interacting Fermi gas. Nature 472, 201–204 (2011)
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)
Jochim, S. et al. Bose-Einstein condensation of molecules. Science 302, 2101–2103 (2003)
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.
The authors declare no competing financial interests.
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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
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