Time evolution of two-mode squeezed vacuum in a single-mode diffusion channel

Based on the infinite sum solution of the master equation corresponding to the diffusion channel we derive the law of time evolution of a two-mode squeezed vacuum state in a single-mode (say a -mode) diffusion channel. We find that the squeezing effect decreases, while two different chaotic field modes emerge. After t time period of the diffusion, the a- mode photon number is larger than b -mode photon number by t kappa, where kappa is the diffusion coefficient, thus by adjusting it, photon number can controlled. Therefore, the diffusion process can be considered a quantum controlling scheme through photon addition.