  The development of microwave photon detectors is paving the way for a wide
range of quantum technologies and fundamental discoveries involving single
photons. Here, we investigate the photon emission from a microwave cavity and
find that distribution of photon waiting times contains information about
few-photon processes, which cannot easily be extracted from standard
correlation measurements. The factorial cumulants of the photon counting
statistics are positive at all times, which may be intimately linked with the
bosonic quantum nature of the photons. We obtain a simple expression for the
rare fluctuations of the photon current, which is helpful in understanding
earlier results on heat transport statistics and measurements of work
distributions. Under non-equilibrium conditions, where a small temperature
gradient drives a heat current through the cavity, we formulate a
fluctuation-dissipation relation for the heat noise spectra. Our work suggests
a number of experiments for the near future, and it offers theoretical
questions for further investigation.
