Hybrid Atom--Photon Quantum Gate in a Superconducting Microwave Resonator

We propose a novel hybrid quantum gate between an atom and a microwave photon in a superconducting coplanar waveguide cavity by exploiting the strong resonant microwave coupling between adjacent Rydberg states. Using experimentally achievable parameters gate fidelities $> 0.99$ are possible on sub-$\mu$s timescales for waveguide temperatures below 40 mK. This provides a mechanism for generating entanglement between two disparate quantum systems and represents an important step in the creation of a hybrid quantum interface applicable for both quantum simulation and quantum information processing.