Cold atoms are a model system to build quantum fields in the lab. A temperature T=0 state of the quantum gas can be seen as vacuum, the (thermal) excitations can be seen as (quasi) particles propagating on this environment. Especially interesting is the creation and thermalization of (quasi-) particles created in the background. Correlations and full distribution functions of quantum observables open up a window in the equilibrium states and the non-equilibrium dynamics of these particles and the quantum fields. In a first set of experiments, we look at a quench which separates a quantum field into two disjoint parts: Splitting a single 1d superfluid into two. A detailed study of non-translation invariant correlation functions reveals that the fundamental quantum noise introduced by this splitting quench leads to a pre-thermalized state , that it spreads throughout the system in a light cone like manner . The relaxed state is described by a generalized Gibbs ensemble . This is verified through phase correlations up to 10th order. In a first set of experiments, we look at two tunnel coupled super fluids which realize the quantum Sine-Gordon model. Studying under which conditions the higher correlation functions factorize  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. 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. When utilized appropriately, the path-integral offers an alternative to the ordinary quantum formalism of state-vectors, selfadjoint operators, and external observers - an alternative that seems closer to the underlying reality and more in tune with quantum gravity. The basic dynamical relationships are then expressed, not by a propagator, but by the *quantum measure*, a set-function mu that assigns to every (suitably regular) set E of histories its generalized measure mu(E). (The idea is that mu is to quantum mechanics what Wiener-measure is to Brownian motion.) Except in special cases, mu(E) cannot be interpreted as a probability, as it is neither additive nor bounded above by unity. Nor, in general, can it be interpreted as the expectation value of a projection operator (or POVM). Nevertheless, I will describe how one can ascertain mu(E) experimentally for any specified E, by means of an arrangement which, in a well-defined sense, filters out the histories that do not belong to E. This raises the question whether in certain circumstances we can claim to know that the event E actually did occur.
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
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