The knowledge of all correlation functions of a system is equivalent to solving the corresponding quantum many-body

problem. If one can identify the relevant degrees of freedom, the knowledge of a finite set of correlation functions is in

many cases sufficient to determine a sufficiently accurate solution of the corresponding field theory. Complete

factorization is equivalent to identifying the relevant degrees of freedom where the Hamiltonian becomes diagonal. I

will give examples how one can apply this powerful theoretical concept in experiment.

A detailed study of non-translation invariant correlation functions reveals that the pre-thermalized state a system of

two 1-dimensional quantum gas relaxes to after a splitting quench [1], is described by a generalized Gibbs ensemble

[2]. This is verified through phase correlations up to 10th order.

Interference in a pair of tunnel-coupled one-dimensional atomic super-fluids, which realize the quantum Sine-Gordon /

massive Thirring models, allows us to study if, and under which conditions the higher correlation functions factorize

[3]. This allowed us to characterize the essential features of the model solely from our experimental measurements:

detecting the relevant quasi-particles, their interactions and the different topologically distinct vacuum-states the

quasi-particles live in. The experiment thus provides a comprehensive insight into the components needed to solve a

non-trivial quantum field theory.

Our examples establish a general method to analyse quantum systems through experiments. It thus represents a

crucial ingredient towards the implementation and verification of quantum simulators.

Work performed in collaboration with E.Demler (Harvard), Th. Gasenzer und J. Berges (Heidelberg).

Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF): SFB FoQuS: F40-P10 and

the EU: ERC-AdG QuantumRelax

[1] M. Gring et al., Science, 337, 1318 (2012);

[2] T. Langen et al., Science 348 207-211 (2015).

[3] T. Schweigler et al., Nature 545, 323 (2017), arXiv:1505.03126