Epidemic growth and Griffiths effects on an emergent network of excited atoms.

Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report 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. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems.