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arXiv:1804.04037 · Physical Review Letters

Sound Propagation in a Uniform Superfluid Two-Dimensional Bose Gas

Jean-Loup Ville, R. Saint-Jalm, É. Le Cerf, Monika Aidelsburger, Sylvain Nascimbène, Jean Dalibard, J. Beugnon

Published Oct 3, 2018• 100 citations
arXivHTMLPDF

Abstract

In superfluid systems several sound modes can be excited, such as, for example, first and second sound in liquid helium. Here, we excite running and standing waves in a uniform two-dimensional Bose gas and we characterize the propagation of sound in both the superfluid and normal regimes. In the superfluid phase, the measured speed of sound is in good agreement with the prediction of a two-fluid hydrodynamic model, and the weak damping is well explained by the scattering with thermal excitations. In the normal phase we observe a stronger damping, which we attribute to a departure from hydrodynamic behavior.

DOI
10.1103/physrevlett.121.145301

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Abstract We theoretically investigate sound modes in a weakly-interacting collisional Bose gas in D dimensions. Using the Landau’s two-fluid hydrodynamics and working within the Bogoliubov theory, we observe the hybridization of the first and second sound modes for D ⩾ 2. To model the recent measurements of the sound velocities in 2D, obtained in the weakly-interacting regime and around the Berezinskii–Kosterlitz–Thouless transition temperature, we derive a refined calculation of the superfluid density, finding a fair agreement with the experiment. In the 1D case, for which experimental results are currently unavailable, we find no hybridization, triggering the necessity of future investigations. Our analysis provides a systematic understanding of sound propagation in a collisional weakly-interacting Bose gas in D dimensions.
Recently, there has been renewed interest in second sound in superfluid Bose and Fermi gases. By using two-fluid hydrodynamic theory, we review the density response χ nn ( q , ω) of these systems as a tool to identify second sound in experiments based on density probes. Our work generalizes the well-known studies of the dynamic structure factor S ( q , ω) in superfluid 4 He in the critical region. We show that, in the unitary limit of uniform superfluid Fermi gases, the relative weight of second versus first sound in the compressibility sum rule is given by the Landau–Placzek ratio for all temperatures below T c . In contrast to superfluid 4 He, LP is much larger in strongly interacting Fermi gases, being already of order unity for T ∼0.8 T c , thereby providing promising opportunities to excite second sound with density probes. The relative weights of first and second sound are quite different in S ( q , ω) (measured in pulse propagation studies) as compared with Imχ nn ( q , ω) (measured in two-photon Bragg scattering). We show that first and second sound in S ( q , ω) in a strongly interacting Bose-condensed gas are similar to those in a Fermi gas at unitarity. However, in a weakly interacting Bose gas, first and second sound are mainly uncoupled oscillations of the thermal cloud and condensate, respectively, and second sound has most of the spectral weight in S ( q , ω). We also discuss the behaviour of the superfluid and normal fluid velocity fields involved in first and second sound.