Interacting Quantum Matter with Rydberg-atom Synthetic Dimensions

Synthetic dimension platforms offer new unique ways of exploring quantum matter.  Building on the recent success from collaborators in building a synthetic lattice of six Rydberg states on a single atom using ultracold ⁸⁴Sr atoms (arXiv:2101.02871), we study the many-body physics that occurs when atoms with internal synthetic lattices are loaded in microtraps. These interact via strong dipole-dipole flip-flop interactions, giving rise to a novel system exhibiting unique properties.  Theoretical studies on a special case of this system, with equal synthetic tunnelings and uniform nearest neighbor flip-flop interactions between adjacent synthetic sites, reveal phase transition into string-like states for certain interaction strengths. With the synthetic dimension build from Rydberg states, the interactions are non-local and site-dependent. In this talk, we discuss the ground state and finite temperature properties of this system. We also discuss possibilities of exploring other kinds of systems with this platform such as having a different tunneling scheme in the synthetic dimension.