Nonequilibrium phase transitions on a dynamical network: Self-Organized Criticality and Anomalous Percolation in a Rydberg facilitated gas

Using the strong interactions of Rydberg atoms combined with an external drive, individual Rydberg excitations in a gas can facilitate others, leading to a cascading excitation “avalanche”. At high densities of the gas, this leads to an active phase with high Rydberg state population. Due to atom loss, the system intrinsically drives itself towards lower densities, approaching the critical point and eventually crossing over into the absorbing phase, where Rydberg excitations remain localized, a phenomenon known as self-organized criticality (SOC).



We study the behavior of the Rydberg gas numerically close to the critical point and obtain several of the critical exponents that characterize the transition. We show that the existence of a critical point and the universal behavior near that point are strongly influenced by the network character of the facilitation process in a gas and by atomic motion.

Considering the frozen gas limit as well as the high-temperature case, we show how the temperature of the gas changes the universality class.

Specifically, we observe evidence for anomalous directed percolation caused by long-range excitation processes (Lévy-flights) with continuously varying critical exponents. Furthermore we predict avalanche events with the same power-law distribution as found in the first works on SOC by Bak, Tang and Wiesenfeld [Phys. Rev. Lett. 59, 381 (1987)].