Many-level Rydberg atoms: strongly correlated dynamics in a synthetic dimension

The last decade has seen tremendous advances in the control and manipulation of laser-trapped arrays of neutral atoms. The manipulation of Rydberg atoms in such arrays has led to great advances in the realms of analog quantum simulation and digital quantum computation. Here we describe how the simple addition of engineered microwave drives to such arrays can lead to a wealth of new few- and many-body phenomena. We describe a set of nascent experiments exploring dynamics of interacting Rydberg atoms along a synthetic (internal state) dimension, touching on interaction-driven phenomena relevant to topology, artificial gauge fields, and disorder-driven localization phenomena. Such microwave manipulation opens up new directions for exploring complex, driven quantum matter and exotic many-body dynamics.