Noisy parametric amplifiers in non-equilibrium thermo field dynamics

Single-mode and two-mode parametric amplifiers under the influence of Markovian environments are studied by means of non-equilibrium thermo field dynamics. In the presence of both parametric coupling and system–environment interaction, the dissipative Heisenberg equations of motion are solved for the optical modes of interest. By making use of the solutions, it is examined whether the noisy parametric amplifiers can exhibit the non-classical properties. Furthermore, it is shown that the two-mode parametric amplifier is equivalent to the two single-mode parametric amplifiers with subsequent beam splitting, even if they are influenced by the environments.