Damping law of photocount distribution in a dissipative channel

Abstract

For a dissipative channel governed by the master equation of density operator}$d\rho /dt=\kappa \left(2a\rho a^{†}-a^{†}a\rho -\rho a^{†}a\right),${\small \ we find that photocount distribution formula at time}$t,${\small \}$p\left(n,t\right)=Tr\left\{\rho \left(t\right):{\left(\xi a^{†}a\right)}^n{e}^{-\xi a^{†}a}/n!:\right\},${\small \ becomes}$p\left(n,t\right)=Tr${\small \ as if the quantum efficiency}$\xi${\small \ of the detector becomes}$\xi e^{-2\kappa t}${\ This law greatly simplifies the theoretical study of photocount distribution for quantum optical field.

arXiv comment3 pages

References in corpus (1)

• Strategies for choosing path-entangled number states for optimal robust quantum optical metrology in the presence of loss