Microwave single-photon detection using a hybrid spin-optomechanical quantum interface

Semiconductor single-photon detectors cannot be straightforwardly adapted for the microwave regime, primarily because microwave photons carry far less energy and thus require cryogenic temperatures and specialized architectures. Here, we propose a hybrid spin-optomechanical interface to detect single microwave photons where the microwave photons are coupled to a phononic resonator via piezoelectric actuation. This phononic cavity also acts as a photonic cavity with either a single embedded Silicon-Vacancy (SiV) center in diamond or an ensemble of these centers, bridging optical single-photon detection protocols into the microwave domain. We model the detection process as a communication channel whose capacity is quantified by the mutual information $I(A;B)$ between the true photon occupancy (A) and the detector outcome (B). Depending on experimentally achievable parameters, simulations predict $I(A;B)$ in the range $0.57\ln (2)$ to $0.67\ln (2)$, corresponding to true-positive (detection) probabilities above 90% and false-positive (dark count) probabilities below 10% per detection interval. These results suggest a viable path to low-noise, high-efficiency single-photon detection at microwave frequencies.