在量子力學發展後期， 理查費曼(Richard Feynman, 1985)建立原子和電磁場在量子尺度上的交互作用模型。2012年諾貝爾物理獎頒給兩位研究原子和離子在共振腔中與真空或光子耦合(此領域稱為共振腔量子電動力學，cavity quantum electrodynamics)的先驅 Serge Haroche 和 David Wineland， 以表彰他們對微觀原子控制的突破與可能帶來的量子技術。本文試圖探討在介觀系統中, 由於和原子諸多的差異， 與共振腔光子耦合的量子電動力學效應。同時也尋找介觀量子電動力學效應可能帶來的應用。為了更明確描述問題，我們主要探討介觀系統在以下三方面不同於原子的特性所帶來的量子電動力學效應。第一，不同於原子與光子的強耦合，多層量子井 (multiple quantum wells) 的半導體激子(exciton)可以進入強耦合的極限也就是極強耦合領域 (very strong coupling regime)。基於半導體系統，我們嘗試探討這個耦合領域的修正和提出可能應用。第二，不同於原子系統，當主動層的能級寬度由於均勻(homogeneous)和不均勻(inhomogeneous)拓寬(broadening)大於光子能級寬度情況下的弱耦合效應修正和可能應用。最後我們探討二維介觀材料下光子與類自旋能谷的耦合及應用。

第一章我們描述三個介觀系統的量子電動力學議題，主要論述在理論分析與工程應用上帶來的影響。第二章我們整理一般原子的共振腔量子電動力學的理論，有這樣的背景下探討如何將這些理論用於分析介觀物理系統的光子電子交互作用以及分析的目的。這篇研究嘗試回答在介觀系統上的問題: 如何作極強耦合效應 (polariton splitting) 的修正? 如何做弱耦合效應(Purcell effect)的修正? 如何在電子類自旋(pseudospin)材料上應用量子電動力學效應來發掘可能應用?
第三章試圖回答第一個問題。我們探討基於砷化鎵(GaAs)的多重量子井激子和共振腔的耦合。首先建立數值模型去解出在外場下激子-光子系統的極化子(exciton-polariton) 波函數和Hopfield coefficients。然後我們用其他文獻的解析解去驗證數值模型的正確性。接著我們提出兩種實驗方法去檢驗極強耦合的存在性。第一，我們提議透過外加側向電場去調制激子的電偶極強度，當外加電場足夠時觀察是否出現從極強耦合領域到純光子 (bare cavity photon) 領域的轉變。實驗上透過量測外加電場下極化子的光激發螢光 (photoluminescence) 訊號後曲線擬合 (curve fitting) 出光子訊號。第二我們提議透過外加垂直磁場去觀察上下極化子分支的反磁能移 (diamagnetic energy shift) 。由於極強耦合會讓上下極化子產生不同激子半徑的改變，如果實驗上可以得到不同的反磁能移就能證明系統展現出極強耦合量子電動力學效應。最後我們用一開始建立的數值模型驗證我們的提議並得到一致的結論。
第四章試圖回答第二個問題。我們探討一個極端的例子: 近紅外光有機染料 (IR-26 dye) 在介電光子晶體共振腔的速率方程式。光學染料由於分子的振動，整體具有相當寬的能級寬度(約80meV)。有機-矽光子晶體共振腔光源使用弱耦合效應(Purcell effect)來提高自發輻射的速率以增加光源的量子效率 (quantum efficiency)。過去在量子點與量子井的文獻使用現象學參數到速率方程式中來描述共振腔效應，以致忽略了電子能級分布寬度遠大於光子能級寬度的事實而得到不精確的結論。我們參考文獻中對電子和光子各自能級寬度積分的方法來計算自發輻射和受激輻射的速率，進一步以數值解速率方程式。許多文獻指出現象學模型和積分模型在量子點和量子井速率方程式給出相當差異的結論，並且建議積分模型較能解釋實驗結果。我們使用積分模型得到有機-矽光子晶體光源具有較高量子效率和高調制速率的結論。最後我們給出基於有限時域差分法(FDTD)模擬得到的元件設計。
第五章試圖回答第三個問題。我們探討二維材料-石墨烯量子點的能谷類自旋 (valley pseudospin) 與光子的耦合，並提議用於實現光子位元到能谷位元的量子位元轉換。我們首先給出光子與量子點能谷的光學躍遷矩陣。接著我們提出在光學共振腔下光子透過吸收和發射與能谷位元作用的模型並寫下系統的波動方程式。為了計算量子態轉換的效率，我們也推導出整個量子過程的良率 (Yield)和保真度 (Fidelity)。最後我們計算整個量子態轉換的最佳化條件，並在考慮實驗設計上可行的參數下得到相當良好的結論。這樣的量子態轉換可以做為用在量子通訊中量子中繼器或是量子計算中量子記憶體的固態可積體化方案。
第六章我們給予結論並指出未來的研究方向。

Cavity quantum electrodynamics (QED) is an exciting field exploring the electron-photon interactions in quantum level. This dissertation is committed to a cross-material study of the cavity QED effects and applications in mesoscopic systems. These systems are studied to investigate the features of mesoscopic emitters distinctive to their atomic counterpart but also of application and fundamental interests including (1) the Purcell effect of broadband emitter、(2) the valley-photon state transfer through entanglement and (3) the RT semiconductor polariton. The first one is the dielectric photonic crystal nanoslot cavity immersed in an organic fluid containing near-infrared dyes, where we study the Purcell effect under broadband coupling. The second is the graphene quantum dot within cavities, where we study the valley-photon interaction and the quantum state transfer. The third is the GaAs quantum well(QW) arrays within distributed Bragg reflectors, where we study the very strong coupling effect of cavity polariton.
For the first system, we examine the cavity enhanced spontaneous emission and the dynamics of broadband coupling of NIR dye and nanocavity by means of a full rate equation model including the complete cavity QED effects. Based on the modeling results, we numerically design an organic-silicon cavity light source in which its mode volume, quality factor, and far-field emission pattern are optimized for energy-efficient, high-speed applications. Dye quantum efficiency improved by two orders of magnitude and 3dB modulation bandwidth of a few hundred GHz can be obtained.
For the second system, we study the photon-trion coupling where a graphene quantum dot is embedded in optical cavity and the cavity enhanced quantum state transfer from photon to valley qubit through entanglement and projection measurement. We model the overall quantum process by means of writing down a coupled Schrodinger equations to include both coherent and damping processes. To give figure of merits for such process, we analytically derive the expression of yield and fidelity for quantum state transfer. Moreover, we proposed a hybrid cavity setup to improve the efficiency of photon-valley entanglement and final state projection. Based on our numerical study we show promising yield and fidelity considering experimental accessible parameters and provide the optimal design conditions for cavity-quantum dot setup.
For the third system, we investigate the very strong coupling (VSC) effect in semiconductor cavity QED system where the QW exciton radius is dramatically modified has been verified by means of a nonlinear numerical optimization technique. Furthermore, we propose two experimental schemes, one by reducing the oscillator strength of QW exciton with an in-plane electric field to recover the bare cavity energy, and the other by inducing the diamagnetic energy shifts in both UP and LP energy branches with a vertical magnetic field to compare their energy difference, and they experimentally provide unequivocal proof of the existence of VSC. Our work offers further insight into the very strong light–matter interaction in semiconductor optical MCs, and the quest of developing a room temperature GaAs polariton laser.

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