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Gaussian correlations emerge in a large class of many-body quantum systemsquenched out of equilibrium, as demonstrated in recent experiments on coupledone-dimensional superfluids [Schweigler et al., Nature Physics 17, 559 (2021)].Here, we present a mechanism by which an initial state of a Rydberg atom arraycan retain persistent non-Gaussian correlations following a global quench. Thismechanism is based on an effective kinetic blockade rooted in the ground statesymmetry of the system, which prevents thermalizing dynamics under the quenchHamiltonian. We propose how to observe this effect with Rydberg atomexperiments and we demonstrate its resilience against several types ofexperimental errors. These long-lived non-Gaussian states may have practicalapplications as quantum memories or stable resources for quantum-informationprotocols due to the protected non-Gaussianity away from equilibrium.

Persistent non-Gaussian correlations in out-of-equilibrium Rydberg atom arrays