Theoretical Research On Quantum Correlation And Quantum Phase Transition In Cavity QED Systems.

Strongly correlated many-particle systems are intensively studied in condensed matter physics. Since their microscopic properties are very hard to access experimentally, artificial structures have been utilized to simulate the related problems in condensed matter physics and important progresses have been achieved in experiment, such as Josephson junction arrays and cold atoms trapped in an optical lattice. But they have limitations since it is challenging to observe their quantum phenomena due to their short space-and time-scales. Therefore, coupled arrays of cavities are chosen to study quantum many-particle systems. Work on coupled arrays of cavities has been mainly focused on simulating the quantum phase tran-sition between Mott-insulator and superfluid, which is characterized by quantum excitation fluctuations. Previous studies have made greatly important achievements, such as strongly correlation, Bose-Hubbard model, quantum phase transition, ground-state entanglement and so on. In this dissertation, we first investigate atomic collective excitations and photonic entanglement in a single cavity. Next, we study coupled arrays of cavities to investigate the Bose-Hubbard model with enhanced nonlinearity and the relations of quantum phase tran-sition, ground-state entanglement and quantum discord. This dissertation consists of four parts and our work include in the chapters from 3 to 6.Part one is composed of Chapters 1 and 2. Firstly, we give a brief introduction the birth and development of quantum optics and review theoretical and experimental progresses on cavity QED and coupled arrays of cavities. Then, we introduce the concept and correla-tions of quantum entanglement and quantum phase transition. Under the necessity of this dissertation, we use two pieces of representative work to introduce the frontier research this dissertation concerns. We also introduce the concept and principle of polatiton technique, adiabatic elimination, three species of entanglement and quantum discord.Chapter 3 alone consists of the second part, in which we study a case of single cavity before we study coupled arrays of cavities. We investigate a double-Lambda atomic ensemble trapped in a cavity consisting of two modes and the frequency conversion and entanglement between the two mode fields. Chapter 4 is the third part, in which we investigate coupled arrays of cavities, each of which contains N four-level atoms. With the region of effective parameters, an effective Hamiltonian can be achieved by adiabatic elimination. According to the previous work introduced in Chapter 2, we consider the detuning of the atomic second level and discuss that we can improve the nonlinearity by adjusting the detuning. Finally, we investigate the dynamics of the system and Mott-insulator-superfluid phase transition. Part four is composed of Chapters 5 and 6, in which we investigate two coupled cavities. In Chapter 5, we study the correlation of entanglement of two atoms in a single cavity and quantum phase transition. In Chapter 6, we investigate the case in which each cavity contains a single two-level atom. Five possible bipartite entanglement were to characterize four regions of the ground state in the previous work, we just employ a single line quantum discord of two atoms in different cavities to distinguish three regions.Finally, the results are summarized and suggestions for future research are outlined.