EIT 實驗對於雙光子共振的穩定度要求甚高，其中Cascade type EIT的雙光子共振條件為兩道雷射光頻的和。本論文的研究主要是利用雷德堡(Rydberg state)電磁波引發透明(electromagnetically induced transparency)的光譜特性，穩定兩道雷射光頻的和，以提供一個穩定的系統做雷德堡EIT的相關實驗。
本論文主要分為三部分:
第一部分(第一到第二章)，介紹此研究的理論背景， Pound–Drever–Hall(PDH)鎖頻方法和可能遇到的問題，到雷德堡EIT的理論簡介，以及我們使用冷原子慢光光譜檢驗鎖頻結果的相關理論
第二部分(第三到第四章)，為實驗的方法與架設，此部分敘述我們是如何穩定兩道雷射(780 nm和藍光雷射)的光頻，以及利用微分光譜訊號初步檢視微分光譜的結果。
第三部分(第五章)為實驗的結果，包含兩種我們最後採用的方法，以及個別利用慢光檢測鎖頻的結果。

Abstract
During the electromagnetically induced transparency (EIT) experiments, it requires very high quality of two-photon detuning stabilization. In cascade type EIT, the two-photon detuning is the sum of detuning from the probe and the coupling. We exploited the property of room-temperature Rydberg EIT to lock the sum of detuning from a 780 nm probe laser and a 480 nm coupling laser.
This thesis contents three main parts:
First, in chapter 1 and chapter 2, I will introduce the principles of PDH scheme and Rydberg EIT. I will discuss the problems which we encountered while exploiting the PDH scheme and illustrate the theoretical background about determining our locking result with cold-atom slow light spectroscopy.
Second, in chapter 3 and chapter 4, I will show the optical and electrical systems we used to lock our lasers and the locking results of each set up from the FM spectra.
Third, in chapter 5, I will demonstrate the cold-atom slow light spectroscopy experiment results.

目錄
致謝..………………………………………………………………………………………1
摘要..………………………………………………………………………………………2
第一章 Pound–Drever–Hall(PDH) 鎖頻介紹
1.1 相位調變..…………………………………………………………………………...6
1.2 PDH 鎖頻方法..…………………………………………………………………….7
1.3 剩餘調幅(Residual amplitude modulation)問題…………………………………….9
1.3.1 偏極失準效應(Polarization misalignment effect)…………………………….10
1.3.2 共振腔效應(Cavity effect)…………………………………………………...13
1.4 利用頻率調變的鎖頻方法是否可以避免剩餘調幅的問題……………………...15

第二章 雷德堡EIT簡介
2.1雷德堡原子簡介……………………………………………………………………..17
2.2 銣(Rb)原子能階與實驗方法………………………………………………………..18
2.3都卜勒效應…………………………………………………………………………..20
2.4 冷原子Cascade EIT 理論…………………………………………………………..22
2.5 冷原子EIT慢光光譜對雙光子偏移(two-photon detuning)的分析…………….…25

第三章 利用PDH方法鎖780 nm雷射
3.1 以波長計鎖780 nm雷射…………………………………………………………...27
3.2 以Rb 原子飽和吸收光譜鎖頻……………………….……………………………29
3.2.1用Toptica的Digilock鎖780 nm雷射…………...…………………………30
3.2.2 用API-010積分器以及SR844 lock-in Amplifier鎖780 nm雷射………..33
第四章 利用PDH方法與原子Rydberg EIT鎖藍光雷射
4.1 wavemeter 鎖 780 nm，熱原子Rydberg EIT光譜鎖480 nm……………………34
4.2以Digilock和Rb飽和光譜鎖780 nm雷射，用API-010積分器及SR844 lock-in Amplifier鎖藍光)…………………………………………………………………....39

第五章 慢光檢測實驗結果
5.1 決定慢光參數……………………………………………………………………….41
5.2 wavemeter 鎖 780 nm與 EIT光譜鎖480 nm 慢光光譜結果…………………...43
5.3 Rb 飽和光譜鎖 780 nm 與 EIT光譜鎖480 nm慢光光譜結果…………………44

第六章 總結……………………………………………………………………………..45

附錄1 相關參數……………………………………………………………………….46
附錄2 960nm晶體EOM的測試報告………………………………………………..50
附錄3 調變EIT的數值模擬………………………………………………………….51
參考資料…………………………………………………………………………………54

參考資料
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