Controlling Of Correlated Two-photon Transport In A One-dimensional Waveguide Coupling To A Hybrid Atom-optomechanical System

Optomechanical system as a new nonlinear photon phonon interaction system is a po-tential quantum device. The photons in cavity optomechanical system demonstrated with the anti-bunching effect because of the radiation pressure from light for mechanical oscillator, similarly to Kerr nonlinearity. Especially under few photons and strongly coupling regime, and this strongly nonlinear interaction may cause powerful anti-bunching effect. However at present technique, the realization of the strong coupling is still a problem. For the few photons and weakly coupling condition, there is still a research shows that optomechanical system can also realize the anti-bunching effect, even a photon blockade. So under weak coupling condition, the study of optomechanical system in quantum information has very important significance.In order to use the nonlinearity control two photons transmission, we explore theoreti-cally the two photons transport in a single-mode waveguide side-coupled to a hybrid atom-optomechanical system. Because of the four-level atomic ensemble can induce nonlinearity, so the introduction of atomic ensemble can further improve the effect of nonlinearity. Our research shows that the nonlinearity induced by the four-level atom only affects the two-photon bound state so that it tends to make the photons antibunching, while the nonlinear radiation pressure couplings affect both the single-photon and two-photon processes so that it can make the photons bunching or antibunching.In this paper, the specific structure is as follows. In the first chapter, we introduce the basic theory of quantum mechanics and quantum optics, include Schrodinger equation, quan-tum state and its representation. Scattering theory and S matrix, the introduction of relevant knowledge of waveguide. Jaynes-Cummings model, adiabatic elimination and bunching and anti-bunching effect. In the second chapter, we mainly introduce the optomechanical systems and the Hamiltonian derivation of some common systems. In the third chapter, we describe our model calculate the efficiency of the transmission and reflection and show our results.