标题： 连续相变过程中序参量的普遍非高斯统计特性的观测 显示英文标题

标题： Observation of universal non-Gaussian statistics of the order parameter across a continuous phase transition

摘要： 第二阶相变由临界标度和普适性表征。 在相变处热力学量的奇异行为，特别是由该相变的普适类的临界指数决定。 然而，临界性质也由序参量在相变过程中的概率分布所表征，在这里预期存在非高斯统计，但尚未得到广泛研究。 在这里，我们利用动量空间中的单原子分辨检测，测量了相互作用晶格玻色气体中连续相变过程中序参量幅度的完整概率分布。 我们发现涨落被一个有效势能所捕获——通过与朗道理论类比，从测量的概率分布中重建出该势能——在超流（有序）相中显示出非平凡的最小值，而在相变点处消失。 此外，我们在相变附近观察到序参量的非高斯统计特性，其特征是高阶累积量为非零且振荡。 我们提供了直接的实验证据，表明这些振荡是普适的，并且数值上显示它们表现出临界标度。 我们的实验是在非均匀系统中进行的，这挑战了以均匀模型为基础的临界性传统理解。 我们的结果强调了序参量统计在探测临界现象和普适性中的关键作用。 显示英文摘要

摘要： Second-order phase transitions are characterised by critical scaling and universality. The singular behaviour of thermodynamic quantities at the transition, in particular, is determined by critical exponents of the universality class of the transition. However, critical properties are also characterised by the probability distribution of order parameter across the transition, where non-Gaussian statistics are expected, but remain largely unexplored. Here, making use of single-atom-resolved detection in momentum space, we measure the full probability distribution of the amplitude of the order parameter across a continuous phase transition in an interacting lattice Bose gas. We find that fluctuations are captured by an effective potential -- reconstructed from the measured probability distribution by analogy with Landau theory -- displaying a non-trivial minimum in the superfluid (ordered) phase, which vanishes at the transition point. Additionally, we observe non-Gaussian statistics of the order parameter near the transition, distinguished by non-zero and oscillating high-order cumulants. We provide direct experimental evidence that these oscillations are universal, and show numerically that they exhibit critical scaling. Our experiments are conducted in inhomogeneous systems, challenging the conventional understanding of criticality, which is primarily based on homogeneous models. Our results underscore the crucial role of order parameter statistics in probing critical phenomena and universality.