After a general introduction to the main features of second sound in 3D and 2D superfluids, I will focus on a recent experiment carried out at the College de France by the team of Jean Dalibard in a weakly interacting 2D Bose gas. In this experiment it has been shown that second sound exhibts an unexpected behavior above the Berezinski-Kosterlitz-Thouless transition and does not show any jump, differently from the predictions of Landau's two-fluid hydrodynamic theory. The experimental results are explained by developing a collisionless RPA approach and are supported by a stochastic (projected) simulation employing the Gross-Pitaevskii equation.
Collisionless sound in a uniform two-dimensional Bose gas, Miki Ota, Fabrizio Larcher, Franco Dalfovo, Lev Pitaevskii, Nikolaos P. Proukakis, Sandro Stringari, arXiv:1804.04032
Sound propagation in a uniform superfluid two-dimensional Bose gas, J.L. Ville, R. Saint-Jalm, É. Le Cerf, M. Aidelsburger, S. Nascimbène, J. Dalibard, J. Beugnon, arXiv:1804.04037