%0 Journal Article %T On solving the quantum many-body problem %A Thomas Schweigler %A Valentin Kasper %A Sebastian Erne %A Bernhard Rauer %A Tim Langen %A Thomas Gasenzer %A J¨¹rgen Berges %A J£¿rg Schmiedmayer %J Physics %D 2015 %I arXiv %X We experimentally study a pair of tunnel-coupled one-dimensional atomic superfluids, which realize the quantum sine-Gordon/massive Thirring models relevant for a wide variety of disciplines from particle to condensed-matter physics. From measured interference patterns we extract phase correlation functions and analyze if, and under which conditions, the higher-order correlation functions factorize into lower ones. This allows us to characterize the essential features of the model solely from our experimental measurements, detecting the relevant quasiparticles, their interactions and the topologically distinct vacua. Our method provides comprehensive insights into a non-trivial quantum field theory and establishes a general method to analyze quantum many-body systems through experiments. %U http://arxiv.org/abs/1505.03126v1