Optimizing single microwave-photon detection: Input-Output theory
  High fidelity microwave photon counting is an important tool for various areas from background radiation analysis in astronomy to the implementation of circuit QED architectures for the realization of a scalable quantum information processor. In this work we describe a microwave photon counter coupled to a semi-infinite transmission line. We employ input-output theory to examine a continuously driven transmission line as well as traveling photon wave packets. Using analytic and numerical methods, we calculate the conditions on the system parameters necessary to optimize measurement and achieve high detection efficiency. 
M. Sch\"ondorf, L. C. G. Govia, M. Vavilov, R. McDermott and F. K.   Wilhelm
quant-ph