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When Rydberg states are excited in a dense atomic gas the mean number ofexcited atoms reaches a stationary value after an initial transient period. Weshed light on the origin of this steady state that emerges from a purelycoherent evolution of a closed system. To this end we consider aone-dimensional ring lattice, and employ the perfect blockade model, i.e. thesimultaneous excitation of Rydberg atoms occupying neighboring sites isforbidden. We derive an equation of motion which governs the system's evolutionin excitation number space. This equation possesses a steady state which isstrongly localized. Our findings show that this state is to a good accuracygiven by the density matrix of the microcanonical ensemble where thecorresponding microstates are the zero energy eigenstates of the interactionHamiltonian. We analyze the statistics of the Rydberg atom number countproviding expressions for the number of excited Rydberg atoms and the MandelQ-parameter in equilibrium.

Thermalization of a strongly interacting 1D Rydberg lattice gas