Photon Statistics of Propagating Thermal Microwaves

In experiments with superconducting quantum circuits, characterizing the photon statistics of propagating microwave fields is a fundamental task. We quantify the $n^{2}\,{+}\,n$ photon number variance of thermal microwave photons emitted from a black-body radiator for mean photon numbers $0.05\,{\lesssim}\,n\,{\lesssim}\,1.5$. We probe the fields using either correlation measurements or a transmon qubit coupled to a microwave resonator. Our experiments provide a precise quantitative characterization of weak microwave states and information on the noise emitted by a Josephson parametric amplifier.