Studies On Quantum Entanglement And Quantum Correlation Dynamics In Photonic Crystals

Quantum information is a new cross subject,which is the combination of thequantum mechanics, information science and computer science. The developmentof quantum information not only has great commercial value but also has a greatprospect of application in our national security system. Quantum entanglement isan important resource in quantum information science, and its developmentdetermines whether the quantum information science has a widen applicationforeground. However the inevitable interaction between the quantum system andenvironment will eventually destroy the quantum entanglement of the wholequantum system. This is the main obstacle in the realization of the quantumcomputer. So we should study on the quantum information in open quantumsystems. In open quantum system theory, entanglement dynamics will presentdifferently because of different reservoir. This dissertation study the entanglementand quantum correlation dynamics of atoms in photonic crystals, concerning onhow to avoid or control entanglement decay in PBG reservoir. This work haspotential application values in quantum information processing and quantumcomputing. The structure of this dissertation is arranged as follows.Chapter1gives the research background of this dissertation. In chapters2and3, we introduce the fundamental conceptions and methods which are relative to ourwork. Chapter2introduces the basic concepts in quantum information science. InChapter3we introduce the fundamental theory of photonic crystals, including theproperty and preparation of photonic crystal and the elementary theory of PBGreservoir. Chapter4,5and6introduce our research achievements in detail.Including:In chapter4, we study the properties of the fidelity of one-qubit operations in amplitude damping channels and reveal their properties as a function of coupling tothe photonic crystal environment. We show that there is a direct connectionbetween the information fidelity and the detuning of the atomic frequency from thephotonic band gap (PBG). When the atomic transition frequency is far inside theband gap, the time evolution of the fidelity maintains asymptotically a steady-statevalue and can be controlled by the controllable PBG environment. We finally studythe entanglement fidelity of the two-qubit system in this quantum channel.In chapter5, we have analyzed the dynamics of two-qubit entanglement withthe two qubits separated at an arbitrary distance and interacting with an isotropicphotonic crystal. Special attention is paid to the effects of the detuning conditionsand the DDI on the entanglement dynamics of the two-qubit system. It has beenfound that, the deeper the atomic transition frequency is in the band gap, the higheris the preserved entanglement; for some initial states, where entanglement isalready constant, the effect of detuning can be to trigger a maximal entanglement.We also find that, the entanglement can also be modified by the DDI between thetwo atoms. Concretely, when the frequency detuning is negative, the entanglementdecreases with the increase of the strength of the DDI. For a positive detuning,however, the strong DDI leads to the increase of the entanglement. Hance, thequbits may be coherently manipulated by the controllable PBG environment toperform some quantum information protocol in nanostructured materials.In chapter6, we have presented a non-Markovian model describing the exactquantum correlation dynamics of two qubits interacting with a common PBGenvironment. Special attention is paid to the effects of detuning conditions and theinitial states on quantum correlation dynamics of the two-qubit system. We haveobserved that, the quantum discord can survive for a long time in PBGenvironment. Concretely, the discord is immune to a "sudden death" and evolvesasymptotically to a definite steady value in the long-time limit. We have also foundthat, the quantum discord can be created on demand in PBG reservoir. The result here gives a clear way on how to control and manipulate the dynamics of quantumcorrelation by the controllable PBG materials. This is quite significant inperforming some quantum information protocol in nanostructured materials.Chapter7denotes the conclusion and prospect.