Avalanche Exponents of Critical Rydberg-Excitation Spreading on a Dynamical Network*

Understanding the universal properties of non-equilibrium phase transitions such as epidemic spreading is a challenging problem of statistical mechanics. Combining the strong interactions of Rydberg atoms with an external laser drive, Rydberg excitations in an ultracold atomic cloud model an epidemic on a dynamical network, where a single excited atom causes other close by atoms to transition to the Rydberg state. At high gas densities, the epidemic spreads through the whole system (active phase), while at low densities the recovery process (decay to ground state) dominates and the epidemic ends quickly (absorbing phase). Both regimes are separated by an absorbing-state phase transition (ASPT), where power-law distributed avalanches can be observed.

 

We study the avalanche distributions at the critical point of the ASPT as a function of the gas temperature by combining simulations and experimental data. For finite velocities, the atoms form a dynamical network on which the Rydberg excitations can be passed on. We show that the universality class of the ASPT changes from directed percolation via anomalous directed percolation to mean-field for increasing gas temperature. Additionally, we investigate if small losses out of the Rydberg state modify the universality class. Our results offer new insights into non-equilibrium phase transitions on dynamical networks.