Damping Law of Photocount Distribution in a Dissipative Channel

For a dissipative channel governed by the master equation of the density operator describing the photon loss, we find that the photocount distribution formula at time t can be related to the initial photocount distribution by replacing the efficiency of the detector ξ with ξe^?2κt, as if the quantum efficiency ξ of the detector becomes ξe^?2κt. This law greatly simplifies the theoretical study of the photocount distribution for quantum optical fields.