產生窄頻雙光子是實現量子通訊的基礎。使用磁光陷阱製備之超冷原子團產生窄
頻雙光子的系統是熱門的研究領域。通常窄頻雙光子的產生是在高OD條件下的超冷原子團，本文嘗試證明在小OD的超冷原子團下也有產生sub-MHz線寬雙光子的潛力，藉由coupling光的失調操控sFWM產生雙光子之能量-時間糾纏性質並驗證其非古典性質，引入綴飾態原子(dressed atom)圖像解釋coupling光的失調對sFWM的影響。最後利用電光振幅調變器達成在雙光子同調時間內調變信號在雙光子波包。

Narrow-band biphoton plays important role in realizing long distance quantum communication. Cold atomic ensembles are one of the promising source candidates of them. Using two-dimensional magneto-optical traps setting up with high optical depths temporally long biphotons are generated previously. In this thesis, we show a method to generate sub-MHz bandwidth biphoton using low optical depth atomic ensembles. By utilizing dressed Eigen states of the atoms and introducing coupling detuning, we are able to control the quantum interference between two spontaneous four wave-mixing channels. Finally we have shown Electro-optical modulation of biphoton wave packet generated from low optical depth atomic ensembles with arbitrary shaping .

第1章 緒論 11
第2章 自發四波混頻(sFWM)理論計算 13
2.1 線性電極化率和三階電極化率 13
2.2 雙光子相關函數 17
2.3 不同regime的雙光子相關函數 21
2.4 Rabi oscillation regime 24
2.5 結論 31
第3章 coupling光失調下的sFWM過程 33
3.1 產生sub-MHz等級線寬的雙光子相關函數 33
3.2 κ在coupling光失調的情況 33
3.2.1 前言 33
3.2.2 當Ωe2π≫γ13時的G2(τ) 40
3.3 綴飾態原子圖像(Dressed Atom Picture) 42
第4章 sFWM實驗架設與EIT量測 45
4.1 磁光陷阱(Magneto Optical Trap) 45
4.2 780nm波段雷射架設 47
4.3 飽和吸收光譜 50
4.3.1 原理與實驗架設 50
4.3.2 微分信號鎖頻系統 52
4.4 注入鎖頻(Injection locking) 54
4.5 sFWM實驗區架設 56
4.5.1 sFWM光學桌架設 56
4.5.2 sFWM雷射時序 57
4.5.3 780nm波段EIT測量結果 59
第5章 雙子光信號量測實驗 60
5.1 coupling光失調下的雙光子信號 60
5.1.1 前言 60
5.1.2 實驗方法與結果分析 60
5.1.3 柯西-施瓦茨不等式 64
5.2 雙光子信號濾頻實驗 66
5.2.1 前言 66
5.2.2 實驗方法與結果分析 66
5.2.3 窄頻標準具實驗結論 69
5.2.4 標準具光路架設與優化 69
5.3 調變雙子光相關函數 74
5.3.1 前言 74
5.3.2 調變雙光子信號實驗 74
5.3.3 電光振幅調變器(EOAM) 75
5.3.4 電光振幅調變雙光子信號實驗架設 77
5.3.5 電光振幅調變雙光子信號實驗結果 77
5.3.6 使用coupling光失調調變雙光子相關函數 78
5.3.7 結論 81
參考文獻 82
附錄一 Dressed state picture 85
附錄二 電磁波引發透明 87
附錄三 標準具 92
附錄四 coupling光失調下G2(τ)推導 95

[1] A.Predojevi'c and M.W.Mitchell. (Spring International Publishing 2015). Engineering the atom Interaction.
[2] FoxMark. (2006). Quantum Optics An Introduction.
[3] Hans-A. Bachor and Timothy C. Ralph. (2004). A Guide to Experiments in Quantum Optics, Second, Revised and Enlarged Edition.
[4] J. Dalibard and C. Cohen-Tannoudji. (1985). Dressed-atom approach to atomic motion in laser light: the dipole force revisited. J. Opt. Soc. Am. B Vol. 2, Issue 11, pp. 1707-1720.
[5] Jianming Wen, Shengwang Du, and Morton H. Rubin. (2007). Spontaneous parametric down-conversion in a three-level system. Phys. Rev. A 76, 013825.
[6] JiefeiChen. (2011). PhD thesis. Manipulating Classical and Nonclassical Light with Cold Atoms. The Hong Kong University of Science and Technology.
[7] L.-M. Duan, M. D. Lukin, J. I. Cirac and P. Zoller. (2001). Long-distance quantum communication. Nature vol. 414, pp. 413–418.
[8] Pavel Kolchin, Chinmay Belthangady, Shengwang Du, G.Y. Yin, and S. E. Harris. (2008). Electro-Optic Modulation of Single Photons. Phys. Rev. Lett. 101, 103601.
[9] Pavel Kolchin, Chinmay Belthangady, Shengwang Du, G.Y. Yin, and S. E. Harris. (2008). Electro-Optic Modulation of Single Photons. PRL 101, 103601.
[10] Petr M. Anisimov, Jonathan P. Dowling, and Barry C. Sanders. (2011). Objectively Discerning Autler-Townes Splitting from Electromagnetically Induced Transparency. PRL 107, 163604.
[11] Petr M. AnisimovP. Dowling, and Barry C. SandersJonathan. (2011). Petr M. Anisimov,1,* Jonathan P. Dowling,1 and Barry C. Sanders2. Phys. Rev. Lett 107, 163604.
[12] ShengWang Du, Jianming Wen, and Morton H. Rubin. (2008). narrowband biphoton generation near atomic resonance. J.Opt.Soc.Am.B 25,C98.
[13] Shengwang Du, Pavel Kolchin, Chinmay Belthangady, G.Y. Yin, and S. E. Harris. (2008). Subnatural Linewidth Biphotons with Controllable Temporal Length. Phys. Rev. Lett. 100,183603.
[14] VeissierLucile. (2013). Quantum memory protocols in large cold atomic.
[15] Vlatko Balic, Danielle A. Braje, Pavel Kolchin, G.Y. Yin, and S. E. Harris. (2005). Generation of Paired Photons with Controllable Waveforms. Phys. Rev. Lett. 94, 183601.
[16] ZhangShanchao. (2013). Ph.D. thesis. Coherent Quantum Interaction between. Department of Physics,The Hong Kong University of Science and Technology.
[17] 李傳毅. (2018). 碩士論文. 以冷原子系統進行量子光的產生與儲存. 國立清華大學物理系.
[18] 陳保鋼. (2015). 碩士論文. 銣8787 原子的二維磁光陷阱之設計及架設. 國立清華大學物理系.
[19] 楊均偉. (2017). 碩士論文. 以冷原子群產生雙光子之理論與實驗架設. 國立清華大學物理系.
[20] 謝宗樺. (2017). 碩士論文. 電磁引發透明：垂直相交之探測及耦合光束之研究. 國立清華大學物理系.