Statistics of Broadband Microwave Photons

Much effort has been put in the conception and fabrication of large bandwidth amplifier such as travelling-wave parametric amplifiers and quasi-particle based SIS junctions. With such device, we can expect new interesting state such as large bandwidth squeezed states to be achievable in the lab, and new measurement tools will be necessary to correctly describe their quantum nature. In this work, we describe how to recover large bandwidth photon statistics from continuous operator measurement in the microwave domain. The proposed solution involves the use of time domain quadrature which are approximated using an on the fly numerical transformation of the 32GSa/s voltage samples. Crucially we show that a large bandwidth photon detector does not correspond, as one might expect, to the sum of monochromatic photo detectors over the same bandwidth. The proposed measure leads to photon statistics no matter if the chosen photon basis is narrow or large in bandwidth.