在量子光學實驗中，線寬窄、相干時間長、亮度高的糾纏光子光源是相當重要的工具，對於檢驗量子力學基本原理的實驗研究和發展量子通訊技術，以及製作量子電腦都具有重要的意義。本文主要通過理論計算和數值模擬對參量降頻轉換的單晶雙共振糾纏光子光源的模態做行為的分析。具體來說，從單模的緩慢變化波包近似方程出發，得到實驗上所需要的耦合方程，並從本來只有單模態的方程推廣成多模態的形式，並用數值模擬的方法分析了此類雙光子光源產生的光子的模態和實驗參數之間的關係，並把分析結果和實驗結果進行比較。

In the experiment of quantum optics, it is important to have a ultra-bright sources of temporally long, narrowband biphotons. it will be a useful tool in verifying fundamental principle in quantum mechanics, developing quantum communication technology or designing a quantum computer. In this article, I will analyze the behavior of monolithic doubly resonant biphoton source by theoretical computing and numerical simulation. More precisely, from the slow varying envelope equation of single-mode, we can get coupling equation of muti-mode. Numerical simulation can tell us the relation between the experiment parameter and the mode of photons. Finally, we compare the results of simulations and experiments.

摘要
致謝
Ch1 簡介 7
1.1目的動機 7
Ch2 非線性晶體之光源 9
2.1非線性效應 9
2.2 自發參量降頻轉換 10
2.3 準相位匹配 11
2.4 單晶雙共振雙光子光源 13
2.5 實驗參數估計 15
2.6 理論與實驗的對照 16
Ch3 共振自發參量降頻轉換 18
3.1光量子化 18
3.2 緩慢變化包絡線近似(slow varying envelope approximation) 19
3.3 SVEA耦合方程式 20
3.4 ABCD矩陣 21
3.5頻譜功率密度(spectral power density)與格勞勃相關函數(Glauber correlation function) 23
3.6 多模態的ABCD及其頻譜功率密度、格勞勃相關函數 24
Ch4 實驗參數與數值模擬 28
4.1 格勞勃相關函數(Glauber correlation function)實驗簡介 28
4.2實驗數據 29
4.3 衰減率(damping rate)與頻譜之關係 31
4.4 雙光子產生率(biphoton rate)與溫度之關係 37
Ch5 討論與總結 41
參考文獻 42

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