Gaussian models provide an excellent effective description of many quantum many-body systems ranging from condensed-matter systems1,2 all the way to neutron stars3. Gaussian states are common at equilibrium when the interactions are weak. Recently it was proposed that they can also emerge dynamically from a non-Gaussian initial state evolving under non-interacting dynamics4,5,6,7,8,9,10,11. Here we present the experimental observation of such a dynamical emergence of Gaussian correlations in a quantum many-body system. This non-equilibrium evolution is triggered by abruptly switching off the effective interaction between the observed collective degrees of freedom, while leaving the interactions between the microscopic constituents unchanged. Starting from highly non-Gaussian correlations, consistent with the sine–Gordon model12, we observe a Gaussian state emerging over time as revealed by the decay of the fourth- and sixth-order connected correlations in the quantum field. A description of this dynamics requires a novel mechanism for the emergence of Gaussian correlations, which is relevant for a wide class of quantum many-body systems. In our closed system with non-interacting effective degrees of freedom, we do not expect full thermalization13,14,15,16,17,18,19. This memory of the initial state is confirmed by observing recurrences20 of non-Gaussian correlations.
