Quantum Model of Photodetection

We consider the probability $P^{\mathrm{}\left(n\right)\mathrm{}}(t_0, t)$ of counting $n$ photoelectrons during any time interval [$t_0, t$] in a photodetection model built in the general framework of quantum field theory. Owing to an equilibrium assumption on the detector state, $P^{\mathrm{}\left(n\right)\mathrm{}}(t_0, t)$ is evaluated from the incident field and some electron-correlation functions. The conditions for $P^{\mathrm{}\left(n\right)\mathrm{}}(t_0, t)$ to be a compound Poisson distribution as expected are discussed. This leads to the definition of coherence properties for the electrons of the detector in connection with the reliability of the detection operation in counting experiments.