Toward programmable long-range interactions with dipolar Rydberg atoms

Many exciting developments, both in quantum simulation and computation, have come out of work leveraging the native dipole-dipole interactions between Rydberg states. To expand on the capabilities of these Rydberg atom arrays, we propose and work toward techniques for a more flexible control of the structure of interactions than the native 1/r^3 dipole-dipole couplings. We approach this goal from two directions: expanding the range of interactions by incorporating a cavity and resculpting the interactions by Floquet engineering. To engineer all-to-all interactions, we present progress toward trapping circular Rydberg atoms in a superconducting millimeter (mm)-wave Fabry-Perot cavity with high-NA optical access, where coupling to a common cavity mode will allow atoms to interact with each other regardless of their locations by emitting and reabsorbing photons.  We also present progress towards reshaping the functional form of native dipolar interactions, leveraging local optical addressing for Floquet-engineering the magnon dispersion relation. Potential applications include simulating J1-J2 lattice spin models and spin-glass models in which sign-changing couplings induce frustration. Long-term prospects include combining both these techniques of mm-wave cavity QED and Floquet engineering into a versatile toolbox for quantum simulation of long-range interacting spin models.