Synthetic Dimensions with Rydberg Atoms

Recent experiments in our collaboration have created synthetic dimensions using Rydberg levels of ultracold ⁸⁴Sr atoms as synthetic lattice sites and microwaves as synthetic tunnelings between the sites. These synthetic dimensions have fully controllable tunnelings and on-site potentials, allowing experiments to study topological band structures and novel many-body physics. To achieve these goals, it is crucial to understand the system beyond an idealized picture, including effects such as unwanted off-resonant levels, terms beyond the rotating-wave-approximation, and decoherence. We theoretically evaluate these and show that they do not present fundamental obstacles to realizing large synthetic dimensions. We will discuss comparisons with ongoing experiments, which have observed topological edge states in the Su-Schrieffer-Heeger (SSH) model consisting of alternating weak and strong tunnelings in 4- and 6-site synthetic dimension systems consisting of pairs of ³S₁,m=0 and ³P₀ levels with principal quantum numbers n=57-59. Interestingly, we find that the decoherence in the synthetic dimension differs qualitatively from typical real space decoherence, which may lead to new phenomena. This establishes the framework in which to study interacting topological models.