Damping law of photocount distribution in a dissipative channel

Abstract

For a dissipative channel governed by the master equation of density operator}$dρ/dt=κ\left(2aρa^{\dagger}-a^{\dagger}aρ-ρa^{\dagger}a\right) ,${\small \ we find that photocount distribution formula at time}$t,${\small \}$p\left(n,t\right) =Tr\left\{ρ\left(t\right) \mathbf{\colon}\left(ξa^{\dagger}a\right) ^{n}e^{-ξa^{\dagger}a}/n!\colon \right\} ,${\small \ becomes}$p\left(n,t\right) =Tr% \left[ ρ\left(0\right) \mathbf{\colon}\left(ξe^{-2κt}a^{\dagger}a\right) ^{n}e^{-ξe^{-2κt}a^{\dagger}a}/n!\colon % \right] ,${\small \ as if the quantum efficiency}$ξ${\small \ of the detector becomes}$ξe^{-2κt}${\ This law greatly simplifies the theoretical study of photocount distribution for quantum optical field.

3 pages