Master equation describing the diffusion process for a coherent state

Abstract

The evolution of a pure coherent state into a chaotic state is described very well by a master equation, as is validated via an examination of the coherent state's evolution during the diffusion process, fully utilizing the technique of integration within an ordered product (IWOP) of operators. The same equation also describes a limitation that maintains the coherence in a weak diffusion process, i.e., when the dissipation is very weak and the initial average photon number is large. This equation is dρ/ dt = −κ[a+aρ −a+ρa − aρa+ + ρaa+]. The physical difference between this diffusion equation and the better-known amplitude damping master equation is pointed out.