Photon enhanced chaotic light and its dissipation in an amplitude damping channel

In this paper, we investigate how a m-photon enhanced chaotic field (PACF), denoted by 1−e−λm+1a†me−λa†aam/m!, evolves in an amplitude damping channel with a damping constant κ. By using the technique of integration within ordered product of operators (IWOP), we find that it evolves into a Laguerre function-weighted chaotic field which is described by ⋮e1−eλe2κtaa†Lmeλ+2κtaa†⋮, which is in antinormal ordering. Time evolution of photon number average and fluctuation in this process are also derived. The corresponding evolution law of the Wigner function is also deduced analytically.