Robust Microwave-Optical Photon Conversion Using Cavity Modes Strongly Hybridized with a Color Center Ensemble

Abstract: A microwave-optical photon converter with high efficiency ($>50$ %) and low added noise ($\ll 1$ photon) could enable the creation of scalable quantum networks where quantum information is distributed optically and processed in the microwave regime. However, integrated converters demonstrated to date lack sufficient co-operativity or are too lossy to provide the required performance. Here we propose a bi-directional microwave-optical converter employing an ensemble of spin-bearing color centers hosted within a high-Q Si photonic resonator and coupled magnetically to a high-Q superconducting microwave resonator. We develop a theory for microwave-optical conversion when the ensemble of centers is strongly hybridized with one or both cavities, and find a counterintuitive operating point where microwave and optical photons are tuned to bare center/cavity resonances. Compared to the perturbative coupling regime, we find a substantially enhanced nonlinearity, making it possible to obtain the required co-operativity with reduced pump- and center-induced losses, and improved robustness to optical inhomogeneous broadening. Taking color center and optical pump-induced losses into account in both the Si photonic and superconducting resonators, we find that $\sim 95$ % total efficiency and added noise $\ll 1$ quanta is possible at low ($\mu$W) pump powers for both Er- and T-centers in Si. Our results open new pathways towards quantum networks using microwave-optical converters.