以低溫原子(溫度約300μK)為實驗系統，本論文的研究工作主要是探討雷德堡態(Rydberg state)電磁波引發透明(electromagnetically induced transparency，簡稱EIT)光譜之特性。在此EIT激發架構下，探測雷射場(probe laser field)驅動銣87原子基態至5P3/2激發態的躍遷，耦合雷射場(coupling laser field) 驅動5P3/2激發態至雷德堡態的躍遷。
第一部份(第一章)簡介雷德堡原子的物理特性，其中主量子數(principle quantum number)是個重要的參數，其對其他物理量的關係會在這章介紹，接著進一步探討上述特別的物理特性對原子能階的影響。
第二部份(第二到四章)介紹冷原子EIT的理論，以及製備冷原子團所需的實驗架設，並藉由Λ型態EIT光譜優化我們的冷原子系統，讓我們對實驗參數有定量的掌握，為雷德堡態冷原子光譜打下基礎。
第三部份(第五章)是主要的實驗結果，探討原本在Λ型態EIT中符合理論預期的參數在雷德堡態時是否仍有類似結果，並對不同主量子數做量測，若能吻合理論預測，則可依此優化冷原子雷德堡態EIT，達到增強光與原子群交互作用的目的，在未來量子資訊的發展上更進一步。

We studied the spectrum of Rydberg state electromagnetic induced transparency (EIT) in the low temperature regime (300μK) with 87 Rubidium atoms. Our EIT system is composed of a probe field, which drives the transition from ground state to a 5P3/2 excited state, and a coupling field, which drives the transition from 5P3/2 excited state to Rydberg state.
In the first part (CH1), we introduce the characteristic of Rydberg atoms. Principle quantum number is one of the important parameters of Rydberg atoms, which is associated with many physical quantities. The relation between them would be explained in this part.
The second part (CH2, 3, 4) can be divided into two pieces, theory and experiment. The theoretic part is about the theory of EIT and the method of preparing cold atom. The experimental part would explain the setup of magnetic optical trap (MOT) and the way how to optimize the lambda type EIT system in detail, which gives us the solid base of researching Rydberg state EIT.
The final part (CH5) is the most important experimental result of Rydberg state EIT spectrum. We would verify whether or not Rydberg state EIT spectrum behavior is still the same as the one in lambda type EIT. Further, we can follow the same way in CH4 to optimize the Rydberg state EIT system.

誌謝 1
摘要 2
第一章 雷德堡態原子簡介 5
1.1 雷德堡態原子的物理特性 5
1.2 阻絕效應(Blockade effect) 7
1.3 雷德堡態能階對應頻率以及拉比頻率的計算 9
第二章 冷原子電磁波誘發透明效應(EIT)介紹 11
2.1 銣原子(Rb)能階 11
2.2 磁光陷阱(Magneto-optical trap，簡稱MOT) 12
2.3 冷原子Cascade EIT的理論 14
2.4 非零溫原子的Cascade EIT的理論 19
第三章 實驗架設 27
3.1 雷射系統及元件架設 27
3.2 時序設置 34
第四章 Λ型態EIT的優化 39
4.1 原子數最佳化 39
4.2 黑暗型磁光陷阱(Dark MOT) 41
4.3 γ最佳化 43
4.4 實驗結果 47
第五章 雷德堡態EIT光譜 52
5.1 開關耦合雷射的AOM之漏光效應 52
5.2 溫度對EIT光譜影響之理論分析 56
5.3 不同耦合光功率和主量子數的EIT光譜 58
5.4 不同OD下的EIT光譜 64
參考資料 67

[1] Thomas F. Gallagher, “Rydberg Atoms”, Cambridge University Press, Cambridge, (1994)
[2] J. D. Pritchard, K. J. Weatherill, C. S. Adams, “Non-linear optics using cold Rydberg atoms”, Annual Review of Cold Atoms and Molecules, 1, 301 (2013)
[3] Thibault Peyronel, Ofer Firstenberg, Qi-Yu Liang, Sebastian Hofferberth, Alexey V. Gorshkov, Thomas Pohl, Mikhail D. Lukin & Vladan Vuletić, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms”, Nature 488, 57–60 (2012)
[4] Markus Mack, Florian Karlewski, Helge Hattermann, Simone Höckh, Florian Jessen, Daniel Cano, József Fortágh, “Measurement of absolute transition frequencies of 87Rb to nS and nD Rydberg states by means of electromagnetically induced transparency”, Phys. Rev. A 83, 052515 (2011)
[5] I. I. Beterov, I. I. Ryabtsev, D. B. Tretyakov, and V. M. Entin, “Quasiclassical calculations of blackbody-radiation-induced depopulation rates and effective lifetimes of Rydberg nS, nP, and nD alkali-metal atoms with n≤80”, Phys. Rev. A 80, 059902 (2009)
[6] J. Deiglmayr, M. Reetz-Lamour, T. Amthor, S. Westermann, A.L. de Oliveira1, M. Weidemüller, “Coherent excitation of Rydberg atoms in an ultracold gas”, Opt. Comm. 264. 293 (2006)
[7] Daniel Adam Steck, “Alkali D Line Data”, http://steck.us/alkalidata (2008)
[8] 毛禮富, “黑暗型磁光陷阱的發展與研究”, 國立清華大學, 碩士論文 (1998)
[9] 游秩群, “熱原子的電磁波引發透明光譜及冷原子的四波混頻過程相位不匹配之理論研究”, 國立清華大學, 碩士論文 (2014)
[10] 賴怡樺, “四波混頻的雙光子備製與室溫原子的雷德堡-電磁波引發透明光譜”, 國立清華大學, 碩士論文 (2016)
[11] 莊雅雯, “雷德堡電磁波引發透明效應之研究”, 國立清華大學, 碩士論文 (2015)
[12] J. D. Pritchard, D. Maxwell, A. Gauguet, K. J. Weatherill, M. P. A. Jones, and C. S. Adams, “Cooperative Atom-Light Interaction in a Blockaded Rydberg Ensemble”, Phys. Rev. Lett. 105, 193603 (2010)
[13] Aaron W. Reinhard, “Cold Rydberg-Atom Interactions”, The University of Michigan, Doctoral dissertation (2008)