Quantum Nature And Calculations For Coupled Cavity Array Systems

Photon is an excellent information carrier.They do not directly interact with each other,be able to travel at the speed of light in vacuum and medium over long distances with little decoherence,etc.All these advantages makes it be widely used in modern communications.However,with the progress of science and technology,especially the quantum communication technology,researchers put more stringent demands on photon transmission and manipulations.Among the many solutions,the coupled resonator waveguide technology allows the photon to be well isolated from the outside world,which effectively reducing the decoherence effect of the environment.At the same time,it can improve the efficiency of the interaction between photons and matter,providing good ways for people to control the photons.These factors make this technology one of the most popular solutions.In this paper,the properties of the coupled resonator waveguides for different polarized photons,the properties of quantum entanglement and the nonlocality are studied in detail.In addition,in the theoretical derivation calculations,we propose a programming method to solve the problem of Hamiltonian matrix expression in finite Hilbert space.The main contents are as follows:1.We summary the formation,development,the remarkable achievements of quantum mechanics theory,and the background of quantum computing and quantum communication technology.Since qubits are very important in quantum computation and communication,we introduced it in detail.The coupled resonator waveguide are introduced in detail theoretically and experimentally.2.We introduce some of the basic knowledge associated with computing and some of the properties that are closely related to quantum systems.Afterwards,we introduce the Hilbert space,which provides us a platform linking the real physical systems with the mathematical tools.Then,we make some illustrations about the postulates in quantum mechanics.After introducing these basic rules,we discuss some of the properties of the quantum system that will be covered later in this paper.We introduce the von Neumann entropy to measure the quantum entanglement,and introduce the Bell inequality method to study the nonlocalities of our quantum system.3.We analyzed the coupled resonator waveguide system in detail and study the phase transition in the ground state of quantum system referring to the concept of entropy in information theory.Then we study the entanglement problem between the different subsystems in the ground state.In order to carry out the quantitative calculation and description,we choose the von Neumann entropy method for further study.Finally,we study the phenomenon of nonlocalities of the quantum sy stem and make a detailed calculation about the CHSH inequality.When the quantum entanglement between subsystems is very small,the classical association between them plays a major role.Quantum phenomena can only be observed if the quantum association between the subsystems is strong enough.4.We focus on the programming method of solving the matrix representation of Hamiltonian for finite dimensional quantum systems.It consists of two steps:finding all the state vectors spanning the Hilbert space of the system;calculating the matrix elements.When it comes to building a Hilbert space,we introduce the mixed radix systems to save memory.When it comes to calculating matrix elements,we take a detailed quantum system as an example for illustrations.After explaining our programming methods,we choose some typical physical systems to practice the methods described above and study the effect of different parameters of the system on the evolution of quantum states.