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Observation of first and second sound in a BKT superfluid

A Publisher Correction to this article was published on 02 August 2021

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Superfluidity in its various forms has been of interest since the observation of frictionless flow in liquid helium II1,2. In three spatial dimensions it is conceptually associated with the emergence of long-range order at a critical temperature. One of the hallmarks of superfluidity, as predicted by the two-fluid model3,4 and observed in both liquid helium5 and in ultracold atomic gases6,7, is the existence of two kinds of sound excitation—the first and second sound. In two-dimensional systems, thermal fluctuations preclude long-range order8,9; however, superfluidity nevertheless emerges at a non-zero critical temperature through the infinite-order Berezinskii–Kosterlitz–Thouless (BKT) transition10,11, which is associated with a universal jump12 in the superfluid density without any discontinuities in the thermodynamic properties of the fluid. BKT superfluids are also predicted to support two sounds, but so far this has not been observed experimentally. Here we observe first and second sound in a homogeneous two-dimensional atomic Bose gas, and use the two temperature-dependent sound speeds to determine the superfluid density of the gas13,14,15,16. Our results agree with the predictions of BKT theory, including the prediction of a universal jump in the superfluid density at the critical temperature.

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Fig. 1: Sound excitations in a homogeneous two-dimensional Bose gas.
Fig. 2: First and second sound.
Fig. 3: The sound speeds and the superfluid density.

Data availability

The data that support the findings of this study are available in the Apollo repository ( Any additional information is available from the corresponding authors upon reasonable request. Source data are provided with this paper.

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We thank J. Man for experimental assistance; and R. P. Smith, J. Dalibard, M. Zwierlein, R. J. Fletcher, T. A. Hilker, S. Nascimbene and T. Yefsah for discussions. This work was supported by the EPSRC (grant nos EP/N011759/1 and EP/P009565/1), ERC (QBox) and QuantERA (NAQUAS, EPSRC grant no. EP/R043396/1). J.S. acknowledges support from Churchill College (Cambridge), and Z.H. acknowledges support from the Royal Society Wolfson Fellowship.

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P.C. led the data acquisition and analysis. M.G. and J.S. contributed to the data acquisition. P.C., M.G., R.L. and J.S. contributed to the experimental setup. P.C., N.D. and J.S. produced the figures. Z.H. supervised the project. All authors contributed to the data analysis, interpretation of the results and writing of the manuscript.

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Correspondence to Panagiotis Christodoulou.

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Christodoulou, P., Gałka, M., Dogra, N. et al. Observation of first and second sound in a BKT superfluid. Nature 594, 191–194 (2021).

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