在參量降頻轉換這個過程中，準相位匹配是一項很重要的機制之一，然而在現今眾多的實驗與理論中，並沒有明確地指出當在晶體週期性極化的過程中，這些製程上的誤差會對於產生出的光子對它們的量子特性有何影響。
因此，在本篇論文中，我們將深入探討這些誤差所帶來的非理想性與隨機性的準相位匹配，想知道對於這些產生出的糾纏光子對會有何種效應，因此，我們在實驗中量測了糾纏光子對的光譜分佈， 並且提出了一套理論模型解釋我們所觀察到的現象，最後也對於這些光子對，進行了量子力學特性上的量測，如反關聯性參數(α_2d)以及Franson-type干涉。此外，本論文內容以發表於Scientific Reports 6,26079(2016)

Quasi-phase-matching (QPM) has enriched the capacity of parametric down-conversion (PDC) in generating biphotons for many fundamental tests and advanced applications. However, it is not clear how the non-idealities and randomness in the QPM grating of a parametric down-converter may affect the quantum properties of the biphotons. This thesis intends to provide insights into the interplay between PDC and non-ideal or random QPM structures. Using a periodically poled nonlinear crystal with short periodicity, we conduct experimental and theoretical studies of PDC subject to non-ideal duty cycle and random errors in domain lengths. The work described in this thesis has been published in Scientific Reports 6, 26079 (2016)

摘要 1
致謝 3
第一章 實驗動機與目的 8
第二章 理論背景 9
2-1非線性光學 9
2-2耦合方程組 13
2-3相位匹配 17
2-4糾纏性 30
2-5反關聯性參數 34
2-6 Franson-type 干涉儀 36
第三章 量測儀器簡介與參數估計 43
3-1 自發型參量降頻轉換之光源製備 43
3-2 單光子偵測器 46
3-3 重合計數器 48
第四章 實驗架設與數據分析 55
4-1 非理想與隨機性準相位匹配 55
4-2反關聯性參數 67
4-3 Franson-type 干涉儀 72
第五章 結果與討論 78
參考文獻 79

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