Influence of disordered and anisotropic interactions on relaxation dynamics and propagation of correlations in tweezer arrays of Rydberg dipoles

We theoretically investigate the out-of-equilibrium dynamics of irregular one- and two-dimensional arrays of Rydberg dipoles featuring spatially anisotropic interactions. Starting from a collectively polarized initial state, we map out the dynamical phase diagram and identify a crossover between regimes of regular and anomalously slow relaxation of the initial collective order, that strongly depends on both the degree of interaction disorder and anisotropy. In addition, we find the regime of slow relaxation is characterized by a sub-ballistic propagation of correlations that remained confined to short distances even at long times. To explain our findings we develop an analytic model based on decoupled clusters of interacting dipoles that goes beyond prior theoretical works and enables us to identify multiple relaxation timescales. Our findings can be relevant for a wide variety of quantum science platforms naturally featuring disordered dipolar interactions, including polar molecules, frozen Rydberg gases and NV centers.