Abstract
Quantum fluctuations play a central role in the properties of quantum matter. In non-interacting ensembles, they manifest as fluctuations of non-commuting observables, quantified by Heisenberg inequalities. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement arise. In the context of many-body physics, the Bogoliubov theory provides us with an illuminating microscopic picture of how this occurs for weakly-interacting bosons, with the appearance of the quantum depletion formed by pairs of bosons with opposite momenta. Here, we report the observation of these atom pairs in the depletion of an equilibrium interacting Bose gas. A quantitative study of atom-atom correlations, both at opposite and close-by momenta, allows us to fully characterise the equilibrium many-body state. We show that the atom pairs share the properties of two-mode squeezed states, including relative number squeezing. Our results illustrate how interacting systems acquire non-trivial quantum correlations as a result of the interplay between quantum fluctuations and interactions
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