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From classical to quantum non-equilibrium dynamics of Rydberg excitations in optical lattices

The glass phase and its quantum analog are prominent challenges of current non-equilibrium statistical mechanics and condensed matter physics. As a model system to study the transition from classical to quantum glassy dynamics, we propose a setup of laser driven three-level atoms trapped in an optical lattice. Tuning the strength of the laser driving to the intermediate level allows one to study the transition from a classical Kinetically Constrained Model to the coherent regime. For strong driving, Rydberg excitations evolve analogously to defects in the One-Spin Facilitated Model, a minimal model known to exhibit glassy dynamics. In our setup, the constraints result from the interplay between Rydberg interactions and the laser detuning from the Rydberg state. The emerging heterogeneous relaxation timescales are tuneable over several orders of magnitudes. In the opposite limit of weak driving of the intermediate level, we find an effective cluster model which describes the dynamics in a reduced subspace of the allowed number and positions of Rydberg excitations. This subspace is uniquely determined by the initial state and is characterized by a fixed number of clusters of Rydberg excitations. In addition, we investigate the influence of random fields on the classical relaxation. We find that the glassy dynamics can relax faster in the presence of weak random fields.