The Nonclassical Effects In Coupled Cavity Optomechanical Array

When the body is subjected to optical radiation, it will experience a force, which is called the light radiation pressure effect. Radiation pressure is proportional to light intensity and is inversely proportional to the mass, if the light intensity is stronger, the mass is the smaller, the radiation pressure effect will be more obvious. With the development of quantum optic-s, in theory, it provides us a profound understanding of the method of interaction between light and matter, on the other hand, the development of nanoscience and the semiconductor industry in advanced materials, the manufacture of ultra-sensitive micro and nano devices is available, these devices even can be done on atomic scale. These two aspects are combined to form a "Quantum optomechanics". Optical cavity, enhanced by the light field (or micro-cavities), which has a movable reflected mirror, naturally, becomes a significant system to investigate optical radiation pressure effects. The entanglement of mesoscopic even macro-scale objects (mechanical oscillator) is an important issue in quantum mechanics, because it is related to how the scale is a quantum world. In optomechanical system, the interaction between light and harmonic oscillator leads to a lot of interesting effects such as the elec-tromagnetically induced transparency, the entanglement between the mirror and cavity field and the nonlinearity of the field. This system has become an important quantum device. By researching the system, it has theoretical and practical significance to its application in quantum information process.We discuss a N cavity optomechanical array system, by using the adiabatic elimination method and Schrodinger equation, we get an effective Hamiltonian in XX form that only contains mechanical resonator modes. In the case of dissipation, due to the exists of inter-action between the dual-mode and single-mode, the squeezing exists not only between the dual-mode, also resided in two separate modes. As a result of the adjacent lattice jumps and nonlinear radiation pressure, the second-order correlation of single and dual mode compete with each other, the intermode exhibits antibunching which might be used as a single phonon channel. This paper is consist of four chapters. In the first chapter, we introduce the ba-sic theory of quantum optics and quantum information, including the Schrodinger equation, quantum entanglement, quantum entanglement criterion and its measurement, adiabatic e-limination method, the effective Schrodinger equation, cavity QED system and the squeezing of single-mode and two-mode. In the second chapter, we analyze the radiation-pressure inter- action between an optical cavity mode and a mechanical oscillator in classical and quantum framework. In the third chapter, we give the second order correlation function of the light field. To illustrate the bunching and the basic characteristics of the bunching we discuss the delay and zero correlation functions, The fourth chapter is our main research work. In this chapter, we investigate a coupled array of N identical cavity optomechanical systems. By adiabatic eliminating the cavity fields, we derive an effective Hamiltonian of the N phonon modes coupled via XX form. Nonclassical characters have been shown such as state trans-form, single-mode and intermodal quadrature squeezing, single-mode and intermodal second order correlation. Our results show that the single-mode and intermode can display squeezing simultaneously. This property does not exist in the process of nondegenerate parametric down conversion. The intermode exhibits antibunching which might be used as a single phonon channel. It has a great significance for quantum communication, the precision detection of light signals and the boundary between quanta and classics.