Josephson-based scheme for the detection of microwave photons

We propose a scheme for the detection of microwave induced photons through current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the Signal-to-Noise-Ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.