Dynamic Evolution And Non-classical Property For The Interaction System Of Light Field With Matter

In the first part of this paper, the unitary time-evolution operator method has been used to the two-level atom system with the particle dissipation. This approach provide a complete solution for the master equation of the reduced density matrix of the J-C model in the non-perturbation theory framework in which there have been the gain and the dissipation process.In the second part, we have considered the polariton system described by the model effective Hamiltonian involving single mode photon field interacting with a transverse optical phonon in a more realistic form. On this basis, we have discussed the dynamical evolution of the wave function , the dynamical variables and the non-classical properties for the system in a analytic form for the first time. By the nonlinear interactions of the system, the radiation field initially in the coherent state and the polarization wave field initially in the vacuum state exchange energy in the oscillation form with the time evolution. The radiation field and the phonon field can all exhibit squeezed state with time evolution and their second order squeezing oscillate in a complex periodical form with time evolution. The non-classical property is determined by the nonlinear coupling of the system and depends on the existence of the parts kt(a+b + ab+) and k2(a+b+ +ab) simultaneously. At the same time, we have obtained the new results that the statistical distribution of the photon and phonon can oscillate between super-Possion and sub-Possion distribution in a complex periodical form with time evolution, the nonlinear coupling parts contribute to the non-classical statistical feature. However, when the radiation field is initially in the squeezed vacuum state, the phonon field can exhibit the non-classical high-degree squeezing feature with time evolution, which is determined mainly by the nonlinear coupling part k1In the last part, we have discussed the new ground state, i. e. the two-mode rotational squeezed vacuum state, for the polariton system in the coupled state representation and the new results for the quantum fluctuation have been obtained. We find that both the photon field and the phonon field can show squeezing feature, which reveals the ground state is a non-classical state. Therefor, the new quantum phenomenon that the non-classical dynamic squeezing behavior, the non-classical statistical property and the high order squeezing character of the system can all be interpreted by the evolutionary result of the two-mode rotational squeezed vacuum state.