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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 originate. 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. This conceptually simple example yet lacks experimental confirmation. Exploiting the single particle resolution of our metastable Helium detector, we report the direct observation of pairs of atoms with opposite momenta in the depletion of an equilibrium interacting Bose gas. We show that the pair correlation signal rapidly drops as temperature rises, as expected for the quantum depletion. A quantitative study of the atom-atom correlations, both at opposite and close-by momenta, allows us to fully characterise the quantum correlations in the interacting Bose gas. Our results demonstrate how an equilibrium many-body quantum state acquires specific correlations - those of two-mode squeezed states here - as a result of the interplay between quantum fluctuations and interactions. In addition, the measured amplitudes of the correlation signals reveal sub-poissonian number differences between modes at opposite momenta, an important step towards characterising entanglement in equilibrium many-body quantum states. In the future, our approach can be used to characterize more strongly correlated systems for which a theoretical description is lacking, thus fully entering the realm of quantum simulation.
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