Dead time corrections to photon counting statistics II: Quantum theory

The recent formulation of the quantum theory of photodetection, based on the quantum theory of continuous measurements, is extended to the case of a (nonideal) detector which has non-zero dead time. A general result is proven which expresses the dead time modified counting statistics in terms of the counting statistics of anassociated ideal detector. As an illustration, the dead time corrections to the counting statistics of a single-mode free field are worked out, and these corrections are shown to be identical in form to the dead time corrections for a classical optical field of constant intensity.