Vienna Center for Quantum Science and Technology, Atominstitut, TU Wien, Stadionallee 2, 1020 Vienna, Austria.
Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, 69120 Heidelberg, Germany.
Nature. 2017 May 17;545(7654):323-326. doi: 10.1038/nature22310.
Quantum systems can be characterized by their correlations. Higher-order (larger than second order) correlations, and the ways in which they can be decomposed into correlations of lower order, provide important information about the system, its structure, its interactions and its complexity. The measurement of such correlation functions is therefore an essential tool for reading, verifying and characterizing quantum simulations. Although higher-order correlation functions are frequently used in theoretical calculations, so far mainly correlations up to second order have been studied experimentally. Here we study a pair of tunnel-coupled one-dimensional atomic superfluids and characterize the corresponding quantum many-body problem by measuring correlation functions. We extract phase correlation functions up to tenth order from interference patterns and analyse whether, and under what conditions, these functions factorize into correlations of lower order. This analysis characterizes the essential features of our system, the relevant quasiparticles, their interactions and topologically distinct vacua. From our data we conclude that in thermal equilibrium our system can be seen as a quantum simulator of the sine-Gordon model, relevant for diverse disciplines ranging from particle physics to condensed matter. The measurement and evaluation of higher-order correlation functions can easily be generalized to other systems and to study correlations of any other observable such as density, spin and magnetization. It therefore represents a general method for analysing quantum many-body systems from experimental data.
量子系统可以通过它们的相关性来描述。更高阶（大于二阶）的相关性，以及它们如何分解为低阶相关性的方式，提供了关于系统、其结构、相互作用和复杂性的重要信息。因此，测量这些相关函数是读取、验证和描述量子模拟的重要工具。尽管高阶相关函数在理论计算中经常被使用，但到目前为止，实验主要研究了二阶相关函数。在这里，我们研究了一对隧道耦合的一维原子超流体，并通过测量相关函数来描述相应的量子多体问题。我们从干涉模式中提取了高达第十阶的相位相关函数，并分析了这些函数是否以及在什么条件下可以分解为低阶相关性。这种分析描述了我们系统的基本特征、相关准粒子、它们的相互作用和拓扑上不同的真空。从我们的数据中我们得出结论，在热平衡条件下，我们的系统可以被看作是正弦-戈登模型的量子模拟器，这与从粒子物理到凝聚态物质的多个学科都有关。高阶相关函数的测量和评估可以很容易地推广到其他系统，并研究任何其他可观测量（如密度、自旋和磁化强度）的相关性。因此，它代表了一种从实验数据中分析量子多体系统的通用方法。
