We have discovered a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks.
We show that the competition between facilitated excitation and spontaneous decay of Rydberg excitations results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. The observed dynamics follow a power-law time dependence that parallels that which is empirically observed in real-world epidemics, providing a powerful demonstration of universality reaching beyond physics; (ii) a full description and interpretation of the experiment in terms of an emergent susceptible-infected-susceptible network linking the observed macroscopic dynamics to the microscopic physics; and (iii) the unexpected presence of rare region effects and a dynamical Griffiths phase associated to the emergent network structure, which gives rise to critical dynamics over an extended parameter regime and explains the appearance of power-law growth and relaxation, but with non-universal exponents.