Single photon transmission in strong three-mode optomechanical circulatory system

In the few-photon regime, we theoretically propose a feasible scheme to realize strong coupling optomechanical cycle in a three-mode optomechanical circulatory system (OMCS) comprising of cross-Kerr (CK) type and linear coupling between the corresponding two bosonic modes, meanwhile, where one of the bosonic modes is strongly coherently driven and the rest are weakly driven. A Langevin equation for strong three-mode OMCS is derived by adjusting the parameters of the appropriate strong coherent laser. We show that this strong coupling of optomechanical originates from the strong coherently driven the CK coupling modes, thereby, in coherent state displacement representation enhance the optomechanical coupling and present the strengthen of the nonolinearity. We obtain a set of optimal parameters by full numerical simulation of dynamics matrix, under this condition, minimal strong OMCS that exhibit a single photon perfect non-reciprocal transmission between the two optical modes, and unidirectional transportation inter the optomechanical modes. For a detection field, the system presents optomechanical induced transparency (OMIT) behavior. The presented results can be widely applied to quantum devices such as circulators, diodes, and transistors. Moreover, we brief analysis that a system which consisting of dual mechanical modes and one optical mode, further extend the system to a generalized coupled one-dimensional optomechanical array and arbitrary modes optomechanical loop network. Experimentally, the system has been demonstrated to be achieved through a variety of experimental protocols and configurations, for example optomechanical crystal and integrated quantum superconducting circuit.