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