隨著量子力學的發展，量子資訊漸漸變成一門獨立的學問，尤其在量子通訊的領域中光子扮演了非常重要的角色，因此如何產生良好的單光子以及糾纏光子源可以說是最基本也是最核心的課題。
在本實驗中我們使用高產率時間-能量糾纏光子源，透過Photodetector Post-Selection的方式產生預期detection rates約可為13000(s-1/mW)的高效率偏振糾纏光子，與過去用同晶體得到的探測效率相比仍然算高。我們以CHSH inequality以及CHSH like steering inequality驗證了這對糾纏光子彼此之間具有量子的非局域性以及操控性。最後調變時間-能量糾纏光子之間的頻率以及時間的可區分性，並用HOM 干涉儀去分析調變對總波函數造成的影響。

With the development of quantum mechanics, quantum information gradually became an independent subject. In this subject, photon plays a very important role; therefore, how to build a single photon source and also purity entangled bi-photon source are the core issues of the subject.
We use high detected rate time-energy entangled photons to generate polarization entangled photons with high flux by photodetector post-selection. Then, it is expected to have the detection rate up to 13000(s-1/mW) which is relatively high compared with the previous work. Furthermore, we verified our polarization entangled photons possesses quantum nonlocality and steerability by calculating CHSH inequality and CHSH like steering inequality. In the end, we manipulate either the frequency or time distinguishability between a pair of the time-energy entangled photons to analyze the properties of the total wavefunction with the help of Hong-Ou-Mandel interferometer.

摘要 i
致謝 iii
圖表目錄 vi
第一章　實驗動機 1
第二章　理論背景 2
2-1馬克士威爾方程組(Maxwell’s equations) 2
2-2非線性光學(Non-linear optics) 3
2-2.1非線性效應(Non-linear effect) 3
2-2.2波動方程式(Wave equation) 4
2-2.3自發性參量降頻轉換(Spontaneous parametric down-conversion, SPDC) 6
2-3耦合方程組(Coupled equations) 7
2-4相位匹配(Phase matching) 10
2-4.1相位匹配 10
2-4.2非臨界雙折射相位匹配(Non-critical birefringence phase matching) 11
2-4.3準相位匹配(Quasi-phase matching) 12
2-4.4非理想準相位匹配(Non-ideal quasi-phase matching) 14
2-5量子纏結性(Quantum entanglement) 15
2-5.1純態(Pure state) 15
2-5.2密度矩陣(Density matrix) 16
2-5.3混和態(Mixed state) 17
2-5.4纏結性(Entanglement) 18
2-5.5時間-能量糾纏(Time-Energy entanglement) 19
2-6量子力學的試驗 22
2-6.1 EPR悖論(EPR paradox) 22
2-6.2貝爾定理(Bell’s theorem)與貝爾不等式(Bell’s inequality) 27
2-6.3貝爾態(Bell state) 33
2-6.4 類CHSH操控不等式(CHSH like steering inequality) 34
2-7 偏振糾纏光子的製備 39
2-7.1 Photodetector Post-Selection 39
2-7.2利用補償晶體補償時間上的可區分性 41
2-7.3使用光路補償時間上的可區分性 43
第三章　實驗架設與數據分析 53
3-1 Pump光源架設 53
3-2 時間能量糾纏光子源及其性質 54
3-2.1高產率量子光源 54
3-2.2 相位匹配之溫度與波長 55
3-2.3糾纏光子之頻譜分析 57
3-2.4 反相關係數(Anti-correlation parameter) 59
3-3使用晶體補償時間上的可區分性產生偏振糾纏 62
3-3.1偏振糾纏光子之關聯性量測 63
3-4使用光路補償時間上的可區分性產生偏振糾纏 66
3-4.1馬赫-曾德爾干涉儀(Mach-Zehnder interferometer) 67
3-3.3 Hong-Ou-Mandel interference 70
3-3.4偏振糾纏光子之關聯性量測 75
3-3.5貝爾態的調控 76
第四章 討論與總結 79
參考文獻 80

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