Superfluidity in its various forms has been of interest since the observation of frictionless flow in liquid helium II^1,2. 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 model^3,4 and observed in both liquid helium⁵ and in ultracold atomic gases^6,7, is the existence of two kinds of sound excitation—the first and second sound. In two-dimensional systems, thermal fluctuations preclude long-range order^8,9; however, superfluidity nevertheless emerges at a non-zero critical temperature through the infinite-order Berezinskii–Kosterlitz–Thouless (BKT) transition^10,11, 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 gas^13,14,15,16. Our results agree with the predictions of BKT theory, including the prediction of a universal jump in the superfluid density at the critical temperature.

自从观察到液氦中的无摩擦流动 II ^1,2以来，各种形式的超流性一直受到关注。在三个空间维度上，它在概念上与临界温度下长程有序的出现有关。正如双流体模型^3,4所预测的以及在液氦⁵和超冷原子气体^6,7中观察到的那样，超流的一个标志是存在两种声音激发——第一种声音和第二种声音。在二维系统中，热波动排除了长程顺序^8,9；然而，通过无限阶 Berezinskii–Kosterlitz–Thouless (BKT) 转变，超流性仍然会在非零临界温度下出现^10,11，这与超流体密度的普遍跳跃¹²相关联，而流体的热力学性质没有任何不连续性。BKT 超流体也被预测支持两种声音，但到目前为止还没有通过实验观察到这一点。在这里，我们观察均匀二维原子 Bose 气体中的第一声和第二声，并使用两个与温度相关的声速来确定气体^13,14,15,16的超流体密度。我们的结果与 BKT 理论的预测一致，包括临界温度下超流体密度普遍跳跃的预测。