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研究生：	曾嘉政 Tseng, Jia-Cheng
論文名稱：	基於誘發拉曼散射之光子產生理論研究 Theoretical study on photon generation based on stimulated Raman scattering
指導教授：	陳泳帆 Chen, Yong-Fan
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2020
畢業學年度：	108
語文別：	英文
論文頁數：	71
中文關鍵詞：	拉曼散射、光子對產生、電磁波引發透明
外文關鍵詞：	Raman scattering, Paired photon generation, Electromagnetically induced transparency
相關次數：	點閱：122 下載：20
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我們利用海森堡-朗之萬方程以及馬克斯威-薛丁格方程計算並討論了雙Lambda的四波混頻系統它的光子對產生率的頻譜以及光子對的二階關聯性函數；此外，我們也研究了另一種產生光子對的理論，而這方法是基於誘發拉曼散射。我們在這兩套產生光子對的模型對它們的光子產生率在特定參數下做比較，而在我們透過模擬得到的結果裡，基於誘發拉曼散射的斯托克斯光子產生率是比雙Lambda四波混頻系統的產生率還高的。而這是因為基於電磁波引發透明的四波混頻系統壓抑了真空場的參與，從而壓抑了拉曼過程。

We theoretically discuss paired photon generation in the dual-Lambda four-wave mixing system. Using Heisenberg-Langevin formalism and Maxwell-schr"{o}dinger equation, we calculate the spectral generation rate and second-order correlation function of photon pairs. Besides, we also study the theory of the stimulated Raman scattering which is also a method of generating photon pairs.We compare the photon generation rate of these two schemes with certain parameters. Of special interest to this thesis, the photon generation rate of stimulated Raman scattering is higher than that of the dual-Lambda four-wave mixing system in our simulation. It is because the vacuum noise is depressed in the electromagnetically induced transparency based four-wave mixing system, the Raman process is therefore suppressed.

摘要 i
Abstract ii
誌謝 iii
Table of Contents iv
List of Figures vi
Chapter 1. Introduction 1
1.1 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2. Theoretical model of electromagnetically induced transparency 3
2.1 Two-level
System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1. Mathematical description . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.2. Theoretical calculation . . . . . . . . . . . . . . . . . . . . . . . . 6
2.2 Electromagnetically induced transparency . . . . . . . . . . . . . . . . . . 7
2.2.1. Mathematical description . . . . . . . . . . . . . . . . . . . . . . . 7
2.2.2. Theoretical calculation . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3. Paired photon generation in dual-Lambda system 10
3.1 Description of the paired photon generation . . . . . . . . . . . . . . . . . 10
3.1.1. Description of atoms . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.2. Description of photons . . . . . . . . . . . . . . . . . . . . . . . . 11
3.1.3. The interaction Hamiltonian . . . . . . . . . . . . . . . . . . . . . 12
3.1.4. Heisenberg-Langevin equation . . . . . . . . . . . . . . . . . . . . 12
3.1.5. Maxwell-Schrödinger equation . . . . . . . . . . . . . . . . . . . . 14
3.2 Mathematical calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2.1. 0-th
order Heisenberg-Langevin equations . . . . . . . . . . . . . . 14
3.2.2. 1st order Heisenberg-Langevin equations . . . . . . . . . . . . . . 16
3.2.3. Solving Maxwell-Schrödinger equations . . . . . . . . . . . . . . . 17
3.3 The generation rates of Stokes and antiStokes
lights . . . . . . . . . . . . 18
3.4 Discussion of the generation rates . . . . . . . . . . . . . . . . . . . . . . 21
3.5 Second-order correlation function of the generated fields . . . . . . . . . . 30
Chapter 4. Photon generation based on stimulated Raman scattering 40
4.1 Description of the Stimulated Raman scattering . . . . . . . . . . . . . . . 40
4.1.1. Description of atoms . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.2. Description of photons . . . . . . . . . . . . . . . . . . . . . . . . 41
4.1.3. The Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.1.4. Heisenberg equation for the intermediate states . . . . . . . . . . . 42
4.1.5. Maxwell-schrödinger equation for the Stokes field . . . . . . . . . . 44
4.2 Analytical solution of the Stokes field . . . . . . . . . . . . . . . . . . . . 45
4.2.1. Solving the coupled equations . . . . . . . . . . . . . . . . . . . . 45
4.2.2. Stokes field and its generation rate . . . . . . . . . . . . . . . . . . 47
4.3 Steady-state Raman scattering . . . . . . . . . . . . . . . . . . . . . . . . 49
Chapter 5. Conclusion and outlook 55
References 56
Appendix A. Derivation of Heisenberg-Langevin
equation 58
Appendix B. Derivation of fluctuation-dissipation
theorem 62
Appendix C. Solution of the first-order
atomic operators 64
Appendix D. Transform to the moving frame 66
Appendix E. Anti-Stokes
generation and two-photon
correlation of the DLCZ
protocol 67
                                    

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校內：2021-07-31公開
校外：2021-07-31公開

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