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系統識別號 U0026-0812200911491833
論文名稱(中文) 量子電動力學中的糾纏,消相干與量子相變
論文名稱(英文) Entanglement, Decoherence and Quantum Phase Transitions in QED
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 94
學期 1
出版年 95
研究生(中文) 劉如芬
研究生(英文) Ru-Fen Liu
學號 l2890110
學位類別 博士
語文別 英文
論文頁數 90頁
口試委員 口試委員-張志義
召集委員-張為民
召集委員-許祖斌
口試委員-管希聖
口試委員-楊明峰
指導教授-陳家駒
中文關鍵字 none 
英文關鍵字 qubit  entanglement  decoherence  quantum phase transition  quantum electrodynamics 
學科別分類
中文摘要 none
英文摘要  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.
論文目次 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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