The experimental realisation of large scale many-body systems has seen immense progress in recent years, rendering full tomography tools for state identification inefficient, especially for continuous systems. In order to work with these emerging physical platforms, new technologies for state identification are required. In this work, we present first steps towards efficient experimental quantum field tomography. We employ our procedure to capture ultracold atomic systems using atom chips, a setup that allows for the quantum simulation of static and dynamical properties of interacting quantum fields. Our procedure is based on cMPS, the continuous analogues of matrix product states (MPS), ubiquitous in condensed-matter theory. These states naturally incorporate the locality present in realistic physical settings and are thus prime candidates for describing the physics of locally interacting quantum fields. The reconstruction procedure is based on two- and four-point correlation functions, from which we predict higher-order correlation functions, thus validating our reconstruction for the experimental situation at hand. We apply our procedure to quenched prethermalisation experiments for quasi-condensates. In this setting, we can use the quality of our tomographic reconstruction as a probe for the non-equilibrium nature of the involved physical processes. We discuss the potential of such methods in the context of partial verification of analogue quantum simulators.
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