Antoine Tenart, Gaétan Hercé, Jan-Philipp Bureik, Alexandre Dareau, David Clément

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^{1}. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement arise^{2}. Weak interactions are predicted to deplete Bose–Einstein condensates by the formation of correlated pairs of bosons with opposite momenta^{3,4}. Here we report the observation of these atom pairs in the depletion of an equilibrium interacting Bose gas^{5}. Our measurements of atom–atom correlations, both at opposite and close-by momenta^{6,7}, allow us to characterize the equilibrium many-body state. We also show that the atom pairs share the properties of two-mode squeezed states^{8,9}, including relative number squeezing^{10,11,12}. Our results illustrate how interacting systems acquire non-trivial quantum correlations as a result of the interplay between quantum fluctuations and interactions^{13}.