A Superconducting Detector That Counts Microwave Photons up to Two

We propose a detector of microwave photons which can distinguish the vacuum state, one-photon state, and the states with two or more photons. Its operation is based on the two-photon transition. The detection occurs when a Josephson junction switches from a superconducting to a normal state, which provides a macroscopic voltage. We model the detector theoretically and evaluate its performance.