Phase transitions share the universal feature of enhanced fluctuations near the transition point. Here, we show that density fluctuations reveal how a Bose-Einstein condensate of dipolar atoms spontaneously breaks its translation symmetry and enters the supersolid state of matter—a phase that combines superfluidity with crystalline order. We report on the first direct in situ measurement of density fluctuations across the superfluid-supersolid phase transition. This measurement allows us to introduce a general and straightforward way to extract the static structure factor, estimate the spectrum of elementary excitations, and image the dominant fluctuation patterns. We observe a strong response in the static structure factor and infer a distinct roton minimum in the dispersion relation. Furthermore, we show that the characteristic fluctuations correspond to elementary excitations such as the roton modes, which are theoretically predicted to be dominant at the quantum critical point, and that the supersolid state supports both superfluid as well as crystal phonons.

中文翻译：

---

偶极子量子气体中超流体-超固相变的密度涨落

相变具有过渡点附近波动增加的普遍特征。在这里，我们证明了密度波动揭示了偶极原子的玻色-爱因斯坦凝聚物如何自发地打破其平移对称性并进入物质的超固体状态—一种将超流动性与晶体有序相结合的相。我们在第一个直接就地报告测量超流体-超固体相变之间的密度波动。通过这种测量，我们可以引入一种通用且直接的方法来提取静态结构因子，估计基本激励的频谱以及对主要波动模式进行成像。我们在静态结构因子中观察到强烈的响应，并在色散关系中推断出明显的roton最小值。此外，我们表明，特征涨落对应于基本激发，例如roton模式，理论上被预测在量子临界点占主导地位，并且超固态既支持超流体也支持晶体声子。