Anomalous Directed Percolation Universality of Rydberg Facilitation in a Gas

Rydberg atoms interact strongly over large distances leading to effects such as Rydberg blockade or facilitation. In the facilitation regime the dynamics of the system closely resembles those of epidemics, manifesting a non-equilibrium absorbing-state phase transition between large-scale spreading of excitations and an inactive system.

Using Monte-Carlo simulations of an optically driven Rydberg many body gas in the facilitation regime, we analyze the effects of thermal motion and the network character of the facilitation dynamics in a gas on the universality class of the phase transition. For very high temperatures the system shows mean field dynamics. In the low temperature regime, we show that this phase transition falls into the universality class of directed percolation, provided the underlying network of ground state atoms is above the percolation threshold. With increasing temperature however, long-distance (Levy flight-type) excitations leads the system to display signatures of anomalous directed percolation. If the network of ground state atoms is below the percolation threshold the critical point of the phase transition is replaced by an extended Griffith phase.