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研究生:劉如芬
研究生(外文):Ru-Fen Liu
論文名稱:量子電動力學中的糾纏,消相干與量子相變
論文名稱(外文):Entanglement, Decoherence and Quantum Phase Transitions in QED
指導教授:陳家駒陳家駒引用關係
指導教授(外文):Chia-Chu Chen
學位類別:博士
校院名稱:國立成功大學
系所名稱:物理學系碩博士班
學門:自然科學學門
學類:物理學類
論文種類:學術論文
論文出版年:2005
畢業學年度:94
語文別:英文
論文頁數:90
外文關鍵詞:qubitentanglementdecoherencequantum phase transitionquantum electrodynamics
相關次數:
  • 被引用被引用:0
  • 點閱點閱:251
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  • 下載下載:27
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 In this thesis, we analyze the stability of entanglement under evolution. With quantum electrodynamics which is the fundamental theory of matter and field interaction, we calculate the two-electron scattering process which is one of the main process for current generation of spin entanglement. The analysis on the generation of spin entanglement and the disentanglement effect under evolution of identical particles are presented. The stability of spin singlet state is concluded to the order of v^2/c^2. Furthermore, we turn to another physical system, cavity QED, to discuss the disentanglement effect and the generation of entanglement through spontaneous emission. The finite time generation of entanglement and dynamical suppression of disentanglement have been presented for the system with two atoms in a cavity. The comparisons with two atom being in separate cavities are also discussed. The important of the singlet state is also concluded which strengthens the results from the QED analysis. By using the so-called detuned Dicke model, we point out the incomplete relation between quantum phase transition and the discontinuity of the concurrence. The rigorous proof on the sequential instability of ground state transition for two-atom system is also presented in this thesis.
Contents
Abstract iii
Acknowledgements v

1 Quantum Information and Computation: an overview 1

2 Quantum Entanglement: an introduction ......................11
2.1 Schmidt Decomposition: bipartite and multipartite pure states....11
2.2 Separability: mixed state .........................13
2.3 Entanglement measure and Manipulations of entanglement: concentration and distillation ..........................17
2.4 Quantify entanglement ..........................20

3 The Stability of Spin Entanglement in Non-relativistic QED 22
3.1 Introduction ................................22
3.2 Review of Schmidt Decomposition and Effective Hamiltonian .....24
3.3 The Scattering Process ..........................26
3.4 Higher ¬Order Corrections ..........................27
3.5 Summary .................................30

4 Dynamical Suppression of Disentanglement of Coupled Atoms in Cavity 31
4.1 Introduction ................................31
4.2 Atom-Field Interaction: the Jaynes-Cummings Model .........33
4.3 Multi¬atom System: the Dicke Model ..................37
4.3.1 Derivation the Master Equation: the Born-Markov Approximation ...............................38
4.3.2 The measure of Entanglement and the distillability of entanglement ..............................44
4.4 Dynamical suppression of disentanglement ...............45
4.5 Summary .................................51

5 Quantum Phase Transitions and Entanglement in Dicke Model 52
5.1 Introduction ................................52
5.2 The Single ¬Mode Dicke Model and Its Spectrum ............54
5.3 Sequence of Quantum Phase Transitions in Single ¬Mode Dicke Model58
5.4 QPT vs Entanglement in DDM: Two ¬Atom Case ...........60
5.5 QPT with 1+1 Modes ..........................66
5.6 Summary .................................69

6 Discussions and Conclusions 71

Appendix 74
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