Nonequilibrium Universality of Rydberg-Excitation Spreading on a Dynamic Network

Understanding the universal properties of non-equilibrium phase transitions of spreading processes is a challenging problem. This applies in particular to irregular and dynamically varying networks. We here investigate an experimentally accessible model system for such processes, namely the absorbing-state phase transition (ASPT) of Rydberg-excitation spreading, known as Rydberg facilitation, in a laser-driven gas of mobile atoms. It occurs on an irregular graph, set by the random atom positions in the gas and, depending on temperature, changes its character from static to dynamic. By studying the behavior of the order parameter in [Phys. Rev. Lett. 133, 173401 (2024)] we showed numerical evidence for a crossover from directed percolation (DP) universality through various phases of anomalous directed percolation (ADP) to mean-field (MF) behavior when the temperature of the gas is increased. As the behavior of the order parameter is not sufficient to uniquely determine the universality class, we here analyze the distribution of avalanches - characteristic of non-equilibrium critical behavior - to fully characterize the ASPT. Performing extended numerical calculations and experiments on a cold $^{87}$Rb atom gas we confirm our earlier numerical findings and our phenomenological model that maps the dynamic network to a static one with power-law tails of the distribution of excitation distances. Furthermore we discuss the influence of dissipation, present in the experiment and a necessary ingredient for the self-organization of the system to the critical point. In particular we study the potential modification of the universality class by losses as a function of dissipation strength.