Studies Of Nonclassical Effects In SQUID Quantum Metamaterial System

Metamaterials are materials engineered to have properties that have not yet been found in nature. They are made from assemblies of multiple elements fashioned from composite materials such as metals or plastics. The materials are usually arranged in repeating patterns, at scales that are smaller than the wavelengths of the phenomena they influence. Metamaterials derive their properties not from the properties of the base materials, but from their newly designed structures. Their precise shape, geometry,size,orientation and arrangement gives them their smart properties capable of manipulating electromagnetic waves: by blocking, absorbing, enhancing, bending waves, to achieve benefits that go beyond what is possible with conventional materials. Metamaterial research is interdisciplinary and involves such fields as electrical engineering, electromagnetics, classical optics,solid state physics, microwave and antennae engineering, optoelectronics, material sciences, nanoscience and semiconductor engineering.Quantum metamaterials extend the science of metamaterials to the quantum level. They can control electromagnetic radiation by applying the rules of quantum mechanics. In the broad sense, a quantum metamaterial is a metamaterial in which certain quantum properties of the medium must be taken into account and whose behaviour is thus described by both Maxwell’s equations and the Schr¨odinger equation. Its behaviour reflects the existence of both electromagnetic waves and matter waves. The constituents can be at nanoscopic or microscopic scales, depending on the frequency range(e.g., optical or microwave). In a more strict approach, a quantum metamaterial should demonstrate coherent quantumdynamics. Such a system is essentially a spatially extended controllable quantum object that allows additional ways of controlling the propagation of electromagnetic waves. Quantum metamaterials can be narrowly defined as optical media with the following characteristics:(1) Composed of quantum coherent unit elements with engineered parameters;(2) Exhibit controllable quantum states of these elements;(3) Maintain quantum coherence for longer than the traversal time of a relevant electromagnetic signal.The purpose of this thesis is to nonclassical effects in a quantum SQUID metalmaterial system such as the the excitation sub-Poissonian distribution, the quantum squeezing, quantum correlation and quantum entanglement.The main structure of this thesis is as follows:In the first chapter, we firstly introduce the research background of the quantum SQUID metalmaterial system and present the classical SQUID metalmaterial model and quantum SQUID metalmaterial model, respectively.In the second chapter, we mainly study nonclassical properties of light field in the quantum SQUID metamaterial system. After discussing briefly quantum dynamics of quantum SQUID metalmaterial interacting with microwave photons,we investigate the quantum statistical distribution properties of photons and the quadrature squeezing of the light field in detail.In the third chapter, we mainly devote to nonclassical properties of the quantum SQUID metamaterial. We study in detail the quantum statistical distribution properties of the collective excitations for the quantum SQUID metamaterial and the quadrature squeezing of the the quantum SQUID metamaterial.In the fourth chapter, we focus on quantum correlations and quantum entanglement between the microwave photons and the quantum SQUID metamaterial.We calculate the second-order cross correlation function between the light field and the quantum SQUID metamaterial and discuss the Cauchy-Schwarz inequality whose violation implies the existence of the nonclassical correlation. We then study quantum entanglement between the microwave photons and the quantum SQUID metamaterial for a few kind of typical initial states.In the fifth chapter, we summarize and prospect the thesis.