Interaction-induced freezing in synthetic dimensions realized with Rydberg atom arrays

Synthetic dimensions realized using internal atomic states provide a powerful route to engineering interacting quantum dynamics beyond real-space motion. We present theory describing ongoing experiments with tweezer arrays of interacting Rydberg atoms, in which Rydberg levels form a synthetic dimension. Starting from an initial state with each atom in the central synthetic level, we investigate few- and many-particle dynamics. At weak interactions, the system undergoes a modified quantum walk, whereas strong interactions suppress transport and lead to dynamically frozen configurations with the structure of strings or membranes. In the intermediate regime, richer dynamics emerges, lying in a parameter range that is challenging for classical techniques such as exact diagonalization to capture, thereby highlighting these systems' effectiveness as quantum simulators. We demonstrate, both theoretically and experimentally, the characteristic scales governing string and membrane formation, as well as the competing effects responsible for their dissociation.