Manipulating synthetic gauge fluxes via multicolor dressing of Rydberg-atom arrays

Arrays of highly excited Rydberg atoms can be used as powerful quantum simulation platforms. Here, we introduce an approach that makes it possible to implement fully controllable effective spin interactions in such systems. We show that optical Rydberg dressing with multicolor laser fields opens up distinct interaction channels that enable complete site-selective control of the induced interactions and favorable scaling with respect to decoherence. We apply this method to generate synthetic gauge fields for Rydberg excitations where the effective magnetic flux can be manipulated at the single-plaquette level by simply varying the phase of the local dressing field. The system can be mapped to a highly anisotropic Heisenberg model, and the resulting spin interaction opens the door for explorations of topological phenomena with nonlocal density interactions. A remarkable consequence of the interaction is the emergence of topologically protected long-range doublons, which exhibit strongly correlated motion in a chiral and robust manner.