Statistical properties of binomial and negative-binomial combinational optical field state and its generation in quantum diffusion channel

Abstract

According to the combinational binomial-negative-binomial distribution, we propose a binomial-negative-binomial combinational optical field state, which can be generated in the process of a Fock state |m>m| passing through a quantum-mechanical diffusion channel. We derive the second-order coherence degree formula, g(2)(t) =2-((m2+m)/(m+κt2)), which is the diffusion constant. We find that in the process of the Fock state undergoing quantum diffusion and becoming classical, the corresponding photon statistics evolves from sub-Poissonian distribution to Poisson distribution and finally goes to a chaotic state. We also find that the more photons in the initial Fock state, the longer time is needed for quantum decoherence.