Interacting Quantum Matter with Rydberg or Molecule Synthetic Dimensions

Synthetic dimension platforms offer unique ways of exploring quantum matter.  Building on recent success building a synthetic lattice using six Rydberg states on a single atom in ultracold ⁸⁴Sr atoms (arXiv:2101.02871), we theoretically study the many-body physics of atoms with internal synthetic lattices loaded in microtrap arrays and uniform synthetic tunneling. In this setup, different atoms interact via strong dipole-dipole angular-momentum-exchange interactions. We predict that string-like ground states of finite synthetic width occur in the absence of synthetic tunneling and show that these string-like states survive at finite temperatures and tunneling before phase transitioning into a disordered state. We show that finite-temperature and quantum phase transitions occur, including first-order and second-order transitions, with a rich dependence on tunneling, temperature and size of the synthetic lattice. Furthermore, we will discuss how Rydberg atom and ultracold molecule synthetic dimensions platform opens a wide variety of physics to explore by using different tunneling and level schemes.