Kraus-Form Operator Solution to Nonlinear Master Equation by Virtue of the Nonlinear Thermo-Entangled State Representation*

Our work solves the newly constructed nonlinear master equation dρdt=2κ(1f(N-1)a†ρf(N)a+f(N)aρ1f(N-1)a†aρ-ρaa†),where f(N) is an operator-valued function of N = a†a, for describing the mechanism of evolution in the laser channel at extremely high temperature and derives the infinite operator sum representation of quasi-Kraus operators for the reduced density operator. It also shows that in this nonlinear process the initial nonlinear coherent state (NCS) will evolve into the nonlinear coherent excitation of thermo field, indicating that at extremly high temperature, after passing through the laser channel the NCS (a pure state) evolves into a nonlinear coherent excitation of thermo field (a mixed state, also called displaced chaotic state) by continually absorbing photons from the thermal reservoir. Additionally, universal evolving rules of the mean number of photons, variance in the photon number, relative fluctuation of the number of photons, quantum mechanical second-order degrees of coherence are derived.