  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

Quantum Gases;Atomic Physics