The probabilistic character of the measurement process is one of the most puzzling and fascinating aspects of quantum mechanics. In many-body systems quantum mechanical noise reveals non-local correlations of the underlying many-body states. Here, we provide a complete experimental analysis of the shot-to-shot variations of interference fringe contrast for pairs of independently created one-dimensional Bose condensates. Analyzing different system sizes we observe the crossover from thermal to quantum noise, reflected in a characteristic change in the distribution functions from Poissonian to Gumbel-type, in excellent agreement with theoretical predictions based on the Luttinger liquid formalism. We present the first experimental observation of quasi long-range order in one-dimensional atomic condensates, which is a hallmark of quantum fluctuations in one-dimensional systems. Furthermore, our experiments constitute the first analysis of the full distribution of quantum noise in an interacting many-body system.
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