Experimental characterization of a quantum many-body system via higher-order correlations

Experimental measurements of higher-order correlation functions in many-body systems provide insight into a non-trivial quantum field theory and how it can be implemented in a cold-atom quantum simulation. Quantifying correlations on a quantum chip Ultracold gases of rubidium atoms on a quantum chip are well established analogue quantum simulators of quantum many-body physics. The system has been proposed to be described by a field theory called the sine-Gordon model, but verifying this requires direct measurement of higher-order correlation functions. Knowing all of the correlation functions of a system implies being able to characterize the system and solve the underlying quantum many-body problem. Here, the authors measure the higher-order correlation functions in an ultracold gas on a quantum chip from interference patterns, quantitatively confirming that it can indeed be described by a sine-Gordon model. Their methodology could in principle be applied to many types of quantum systems and hence will help to transform analogue quantum simulators into more quantitative and insightful tools. Quantum systems can be characterized by their correlations 1 , 2 . 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 3 , 4 . The measurement of such correlation functions is therefore an essential tool for reading, verifying and characterizing quantum simulations 5 . 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 6 , 7 , 8 , 9 , 10 , relevant for diverse disciplines ranging from particle physics to condensed matter 11 , 12 . The measurement a