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In the presence of strong dephasing noise the dynamics of Rydberg gasesbecomes effectively classical, due to the rapid decay of quantum superpositionsbetween atomic levels. Recently a great deal of attention has been devoted tothe stochastic dynamics that emerges in that limit, revealing severalinteresting features, including kinetically-constrained glassy behaviour,self-similarity and aggregation effects. However, the non-equilibrium physicsof these systems, in particular in the regime where coherent and dissipativeprocesses contribute on equal footing, is yet far from being understood. Toexplore this we study the dynamics of a small one-dimensional Rydberg latticegas subject to dephasing noise by numerically integrating the quantum Masterequation. We interpolate between the coherent and the strongly dephased regimeby defining a generalised concept of a blockade length. We find indicationsthat the main features observed in the strongly dissipative limit persist whenthe dissipation is not strong enough to annihilate quantum coherences at thedynamically relevant time scales. These features include the existence of atime-dependent Rydberg blockade radius, and a growth of the density ofexcitations which is compatible with the power-law behaviour expected in theclassical limit.

Quantum non-equilibrium dynamics of Rydberg gases in the presence of dephasing noise of different strengths