Progress towards studying many-body systems in Rydberg-atom synthetic dimensions*

Selective field ionization (SFI) has been used recently to study the dynamics of a single particle hopping on a synthetic 1D lattice that is constructed by microwave-coupling several Rydberg atomic states within a single atom [1].  We propose to combine single atoms trapped in optical tweezers with our capability for constructing synthetic manifolds using Rydberg states to simulate and study various phenomena in many-body systems that involve interactions between particles. The long-range dipolar interactions between Rydberg states will enable localized interactions in the synthetic space, opening possibilities for studying systems with novel topological properties [2]. We present progress on the construction of the apparatus, the lasers used to excite the ⁸⁸Sr singlet Rydberg series, and the microwave system to drive Rydberg-Rydberg transitions. The use of a spatial light modulator and an in-vacuo objective to create a uniform array of micron-sized optical tweezers at 532 nm is also discussed.