Controlling Of Entanglement And Quantum Speed Limit Time In Photonic Crystal Reservoirs

Quantum entanglement and quantum-speed-limit time are very important in quantum information.By using the entanglement,many quantum tasks,such as quantum key distribution,quantum teleportation,quantum search algorithm and etc,can be realized.Quantum-speed-limit time captures the intrinsic minimal time interval for a quantum system evolving from an initial state to a target state.It plays a key role in quantum communication,quantum computation and quantum optimal control.Due to the inevitable interaction between an actual quantum system and its surrounding environment,the entanglement of quantum systems will be eventually destroyed.Moreover,the QSL time is strongly dependent on the surrounding environment.So,the studying of entanglement dynamics and the QSL time of open quantum systems,and finding the regulation and control schemes are necessary and meaningful for quantum information processing.In this project,the photonic crystal which is a controlled non-Markovian environment is chosen as a research platform.We study the entanglement dynamics and the QSL time of the quantum systems embedded in photonic crystals,and obtain some useful results.The main points of this thesis are as follows:In Chapter 1,the research background and significance are described briefly.In Chapter 2,we give a brief introduction of basic theory of photonic crystals,including definition of photinic crystals,main characteristics and application,and analytic expression of non-Markovian dynamics in photonic crystals.In Chapter 3,we give a brief introduction of basic theory of quantum information theory,including definition of entanglement,the measure method of entanglement,the QSL time in closed and open quantum systems.In Chapter 4,we study the entanglement manipulation by atomic position in photonic crystals.We consider two entangled atoms,each of which is embedded in a coherent photonic-band-gap(PBG)reservoir.The effect of the atomic embedded position on the entanglement of the two-atom system is studied.We find that theembedded position of the atom plays an important role in the dynamics of entanglement.The variation of the atomic position can lead to the shift between entanglement sudden death and the entanglement trapping.We also consider the entanglement transfer between different subsystems.Our result provides a new parameter for controlling entanglement,and can be guide the relevant experimental study.In Chapter 5,we study the threshold for the formation of atom-photon bound(APB)states.The APB state has potential application prospects in quantum information processing.The existence of APB states can lead to quantum entanglement preservation between atoms as well as permanent effective coupling between reservoir modes.It also provides a new method for the construction of quantum network.So,it is necessary to study the formation of APB state and the controlling method of APB states in photonic crystals.In this chapter,we study the APB state from a two-level atom embedded in a coherent photonic-band-gap(PBG)reservoir,and successfully give the threshold of coupling strength and band-gap width for formation of APB states.The feasible experimental systems for verifying the above phenomena are discussed.Our results provide a clear clue on how to form and control APB states in PBG materials.In Chapter 6,we study the quantum speedup and controlling of QSL time in photonic-band-gap reservoir.For a model of a two-level atom embedded in a photonic-band-gap reservoir,we study the effect of the atomic embedded position,the width of the band gap and the defect mode on the QSL time.We find that,by changing the reservoir parameters,the speedup region lies even outside the band-gap region,where the non-Markovian effect is weak.Our results provide new degree of freedoms to depress the quantum speed limit time in photonic crystals.