Theoretical Study On The Generation Of Continuous Variable Entanglement Via Cavity QED

Quantum entanglement which is provided by quantum mechanics has become the most important and precious resource. It is because of entanglement that people can break through limitations of classical mechanics. and thus can develop information science and technology from a new perspective. e.g.. it can accomplish the task which can not be done by classical communication. The generation of continuous-variable (CV) entanglement is an advanced subject in the field of quantum optics and quantum information. since CV quantum commu-nication can achieve high bit rate. detection efficiency. and big communication band. The research on CV communication has wide application in the future. Therefore. in recent years. the generation of CV entanglement has attracted considerable attention. In addition. cavity QED. with atoms interacting with electromagnetic fields inside a cavity. has been shown to be an important quantum device. In this thesis. the generation of CV entanglement based on cavity QED is investigated theoretically. The thesis is divided into seven chapters. with our work included in the chapters from 3 to 7.In chapter 1. the basic theory of quantum information and the concept of quantum entanglement are introduced, and then the definition. entanglement criterion. application and research situation of CV entanglement are briefly described. At the end of the chapter, the organization of the thesis is given.In chapter 2. the quantum states of field, the quantum theory of the interaction between atom and field are firstly described. then the concept of cavity QED. the derivation and the algebraic approach to master equations are introduced.In chapter 3. a proposal is presented to generate entangled coherent states (ECSs). We consider a strongly driven three-levelâ…¤-type atom dispersively interacting with a two-mode cavity. If the initial state of the atom is prepared in the ground state. under large detuning condition. we obtain an effective Hamiltonian that similar to parametric frequency converter. We show that when one cavity mode is in the vacuum state and the other cavity mode is in the even or odd coherent sate, the two cavity modes will evolve into ECSs. In particular. the maximally ECSs can be generated if one cavity mode is initially prepared in the odd coherent state. The effect of the cavity losses on the entanglement is studied at last. In chapter 4. another method is proposed to produce ECSs in a two-mode single-atom laser. We consider a nonresonant interaction of a three-level A type atom in a two-mode cavity with three strong classical driving fields. If we measure the atomic state at a given time. the two cavity modes will project into macroscopic entangled states from vacuum fields We show that the ECSs can be obtained in a short time dissipation limit. The amount of the entanglement depends on the ratio between the effective coupling constant and cavity dissipation rate.In chapter 5. output entanglement and squeezing of two-mode fields are investigated. We consider a single four-level atom dispersively interacting with a two-mode cavity. Under large detuning condition. we deduce an unitary squeezing operator of the two-mode fields. By means of the input-output theory. we show the output entanglement and squeezing can be achieved. It is found that the asymmetric detuning and asymmetric atomic initial state split the squeezing into two minimum values. and suitable value of the cavity decay rate is needed for achieving maximum degree squeezing.In chapter 6. the generation of output entanglement and squeezing of a single four-level atom inside a low-Q cavity is investigated. Under large detuning condition. we obtain an effective Hamiltonian which represents a Jaynes-Commings interaction and an-Jaynes-Commings interaction. By means of the input-output theory. we show that the output squeezing and entanglement can be achieved. It is found that when the two cavity modes have the same decay rate. the maximum entanglement is insensitive to the cavity decay rate. but can be controlled by adjusting the ratio between the effective coupling constants.In chapter 7. a scheme to generate three-mode continuous-variable entanglement is pre-sented. The system consists of an atomic cloud dispersively interacting with a three-mode optical cavity and three classical fields. We show that genuinely tripartite entanglement with distinct frequencies can be produced at the output. The characters of the tripartite entan-glement are investigated and the effects of the effective coupling constants on the correlation are theoretically analyzed.Finally. the results are summarized and suggestions for future research work are outlined.