Frozen membrane states and chaotic dynamics in few- and many-body Rydberg synthetic dimensions

Optical tweezer platforms permit the design of scalable and robust neutral atom quantum simulators, many with highly tunable arrays of Rydberg atoms. On our recently constructed rubidium-87 tweezer apparatus, we combine the Rydberg states' native resonant dipole-dipole exchanges with microwave drives between levels to realize interactions in a so-called synthetic dimension. We characterize the transition from free gases of Rydberg electrons to frozen states that are immobilized by strong interactions, both for many-atom arrays (quantum membranes) and for few-atom clusters (bound dimers and trimers). We also demonstrate evidence for a chaotic regime at intermediate interactions, characterized by apparent thermalization of macroscopic observables.