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The physics of highly excited Rydberg atoms is governed by blockade orexclusion interactions that hinder the excitation of atoms in the proximity ofa previously excited one. This leads to cooperative effects and a relaxationdynamics displaying space-time heterogeneity similar to what is observed in therelaxation of glass-forming systems. Here we establish theoretically theexistence of a glassy dynamical regime in an open Rydberg gas, associated withphase coexistence at a first-order transition in dynamical large deviationfunctions. This transition occurs between an active phase of low density inwhich dynamical processes take place on short timescales, and an inactive phasein which excited atoms are dense and the dynamics is highly arrested. Weperform a numerically exact study and develop a mean-field approach that allowsto understand the mechanics of this phase transition. We show that radiativedecay --- which becomes experimentally relevant for long times --- moves thesystem away from dynamical phase coexistence. Nevertheless, the dynamical phasetransition persists and causes strong fluctuations in the observed dynamics.

Glassy dynamics due to a trajectory phase transition in dissipative Rydberg gases