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 inequalities¹. In the presence of interactions, additional quantum fluctuations appear, from which many-body correlations and entanglement arise². 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 gas⁵. 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 interactions¹³.

量子涨落在量子物质的性质中起着核心作用。在非交互系综中，它们表现为非通勤可观察量的波动，由海森堡不等式¹量化。在存在相互作用的情况下，会出现额外的量子涨落，由此产生多体相关和纠缠²。预计弱相互作用会通过形成具有相反动量的相关玻色子对来消耗玻色-爱因斯坦凝聚体^3,4。在这里，我们报告了这些原子对在平衡相互作用玻色气体⁵耗尽中的观察结果。我们对原子-原子相关性的测量，包括相反的和靠近的动量^6,7，允许我们描述平衡多体状态。我们还表明原子对共享双模压缩状态^8,9的属性，包括相对数压缩^10,11,12。我们的结果说明了相互作用系统如何获得非平凡的量子相关性作为量子涨落和相互作用¹³之间相互作用的结果。