Generalized two-mode thermal vacuum state for the Hamiltonian of a parametric amplifier derived by the IWOP method

In this paper, we employ the technique of integration within an ordered product of operators (IWOP) to derive a generalized two-mode thermal vacuum state (GTTVS) for the Hamiltonian of a parametric amplifier. Application of GTTVS in calculating the ensemble average is discussed. The result is in agreement with that obtained by using the generalized Hellmann–Feynmann theorem.