  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.
