Cavity Quantum Electrodynamics with Rydberg atoms in superconducting resonators

Neutral atoms in their Rydberg states interact strongly with microwave and millimeter wave (mmwave) photons. Realizing such a coupling in superconducting resonators can enable a fundamentally new regime for atom based cavity quantum electrodynamics (QED). I will describe a cryogenic cold atom experiment where we strongly couple an ensemble of Rb85 atoms to a novel, high-Q, three dimensional mmwave resonator with ample optical access for trapping and addressing atoms [1]. I will show how, by simultaneously coupling the atoms to an optical cavity, we implement a transducer that can convert single millimeter wave photons to optical photons with state-of-the-art efficiency (58 %) and bandwidth (360 kHz) [2]. I will further discuss the prospects for extending these techniques to microwave frequencies and coupling the atoms to transmons, bridging cavity and circuit QED. Finally, I will describe our efforts to use the non-linearity of the atom-resonator interaction to generate spin squeezed states.