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系統識別號 U0026-3006201112482200
論文名稱(中文) 光子網路中的非平衡量子理論
論文名稱(英文) Nonequilibrium Quantum Theory for Photonic Network
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 99
學期 2
出版年 100
研究生(中文) 李振宇
研究生(英文) Chan U Lei
學號 l26984010
學位類別 碩士
語文別 英文
論文頁數 63頁
口試委員 指導教授-張為民
口試委員-周忠憲
口試委員-郭西川
中文關鍵字 非平衡  退相干  光子網路 
英文關鍵字 open quantum systems  nonequilibrium  decoherence  photonic networks 
學科別分類
中文摘要 在本論文中,我們建立了一個非平衡態量子理論去描述光子網路中的量子相干、退相干的動力學和光子的量子傳輸。在本論文中所討論的的光子網路是由具有光子能帶結構的波導與共振腔所組成的全光子電路。對波導的所有自由度取跡,我們得到受外場驅動的共振腔的精確主方程,所有共振腔與波導之間的反作用都完全的由這個精確的主方程所描述。傳輸到波導的光子流可以完全的經由這個精確的主方程所決定。並且,我們得到了受驅共振腔中的光子動子學與光子傳輸之間的關係。所有的非馬可夫效應和量子相干、退相干效應都被完全的包含在本理論之中。本論文中的非平均態量子理論統一了兩個基本的非平衡態方法,凱爾迪西的非平衡態格林函數方法和費曼維儂的影響泛函理論,藉由統合這兩個基本理論讓本理論成為研究光子的量子動力學和量子傳輸的一個強而有力的工具。作為示例,我們應用本理論去研究一個在光子晶體中與波導偶合的納米共振腔的非馬可夫動力學和一個在光子晶體中與兩個波導偶合的受外場驅動的納米共振腔的量子傳輸現象。在光子網路中的受驅共振腔裡的光子相干與光子傳輸的可控性在此例子之中得到展現。
英文摘要 In this thesis, a nonequilibrium quantum theory to describe quantum coherence, decoherence dynamics and quantum photonic transport in photonic networks is developed. The photonic networks concerned in the thesis consist of all-optical circuits incorporating photonic bandgap waveguides and driven resonators. The master equation of the driven resonators is obtained by explicitly eliminating all the waveguide degrees of freedom while the back-reactions between resonators and waveguides are fully taken into account. The photonic transport flowing through waveguides are entirely determined from the exact master equation of the driven resonators. The relations between the driven photonic dynamics and photocurrents are obtained. The non-Markovian memory structure and quantum coherence and decoherence effects in photonic networks are also fully included. This nonequilibrium quantum theory unifies two fundamental nonequilibrium approaches, the Keldysh's nonequilibrium Green function technique and the Feynman-Vernon influence functional approach, together to make the investigation of the quantum dynamics and quantum photonic transport become more powerful. As an illustration, the theory is applied to the non-Markovian dynamics of a nanocavity coupled to a waveguide in photonic crystal and transport phenomena of a driven nanocavity coupled to two waveguides in photonic crystals. The controllability of photonic coherence and photonic transport through the driven resonator is demonstrated.
論文目次 Contents
1 Introduction 4
1.1 Nanophotonics Devices 4
1.2 Open Quantum System and Non-Equilibrium Quantum Dynamics 5
1.3 Thesis Overview 6
2 Modeling of Photonic Networks 8
3 Exact Master Equation 12
3.1 Feynman-Vernon influence functional approach 12
3.2 Equation of motion approach 18
3.3 Solution of the Exact Master Equation 22
3.3.1 Coherent state 23
3.3.2 Thermal state 23
3.3.3 Squeezed vacuum 24
3.3.4 Superposition of coherent states 24
4 Photonic Transport 26
4.1 Photocurrent in each waveguide channel 26
4.2 Relations to the Keldysh's nonequilibrium Green function technique 28
5 Applications : photonic network in photonic crystal 31
5.1 Non-Markovian dynamics of a microcavity coupled to a waveguide in photonic crystal 33
5.1.1 Analytic solutions in both the weak and strong coupling regime 34
5.1.2 Exact numerical solutions 37
5.1.3 Evolution of the Wigner function 43
5.2 Photonic transport in photonic network 50
5.2.1 Analytical solutions in the weak coupling regime 50
5.2.2 Exact numerical solutions in both the weak and strong coupling regimes 54
6 Conclusion and Perspective 59
7 Bibliography 62
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