Observing the Poisson Distribution of a Coherent Microwave Field With a Parametric Photon Detector

Single-photon detectors are essential for implementing optical quantum technologies, such as quantum key distribution, and for enhancing optical imaging systems such as lidar, while also playing a crucial role in studying the statistical properties of light. In this work, we show how the underlying photon statistics can be revealed by using a threshold detector, implemented as a Josephson parametric amplifier operating near a first-order phase transition. We describe the detection protocol, which utilizes a series of pumping pulses followed by the observation of activated switching events. The acquired data are analyzed using two binomial tests, and the results are compared to a theoretical model that takes into account the photon statistics of the microwave field, with additional validation provided by computer simulations. We show that these tests provide conclusive evidence for the Poissonian statistics in the case of a coherent state, in agreement with the experimental data. In addition, this method enables us to distinguish between different statistics of the incoming probe field. Our approach is broadly applicable to standard non-photon-number-resolving detectors, offering a practical pathway to characterize photon statistics in quantum microwave and optical systems.