Disordered Dynamics in Rydberg Tweezer Arrays

We numerically study out-of-equilibrium dynamics in an ensemble of positionally disordered qubits featuring isotropic and anisotropic dipolar interactions, such as that realized by Rydberg atoms in programmable tweezer arrays. We investigate the time evolution of the collective magnetization and propagation of correlations in a disordered quantum spin system prepared initially in a superposition of two different Rydberg states. We map out a dynamical phase diagram of one- and two-dimensional arrays characterized by regimes of slow and fast relaxation of magnetization, indicating a crossover resulting from the degree of interaction disorder in the system. In addition, two-dimensional arrays exhibit richer relaxation dynamics, as the relative anisotropy of the interactions along different directions is tuned to even nearly halt the decay of the collective magnetization, consistent with previous predictions for this system. The propagation of correlations indicates two time scales, each associated with dynamics dominated by pairwise interactions between clusters of two or three spins, while we also observe that long-range correlations are inhibited from developing past a distance that varies with the disorder of the array. Our results demonstrate that the glassy behavior in disordered spin systems is not universal for strong disorder as indicated with two-dimensional arrays, while signatures of glassy dynamics are observable in higher-order correlations that may provide further information about relaxation of the many-body system.