雙Λ型及階梯型四波混頻機制之理論研究｜國立清華大學博碩士論文庫

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研究生：	謝沛軒 Hsieh, Pei-Hsuan
論文名稱：	雙Λ型及階梯型四波混頻機制之理論研究 Theoretical Study on the Double-Λ and the Diamond-Type Four-Wave Mixing Processes
指導教授：	余怡德 Yu, Ite A.
口試委員:	褚志崧 Chuu, Chih-Sung 林晏詳 Lin, Yen-Hsiang 林俊達 Lin, Guin-Dar
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：	2023
畢業學年度：	111
語文別：	英文
論文頁數：	66
中文關鍵詞：	四波混頻、產生雙光子
外文關鍵詞：	Four-Wave Mixing, Biphoton Generation
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本文分別研究雙Λ型系統以及階梯型系統中的四波混頻過程。論文的前三章討論雙Λ型系統中的四波混頻機制，並且聚焦在以理論的方式找出哪些參數條件能夠在雙光子共振點上最大化系統產生之probe光子的光譜訊號。更精確地說，我們計算出在固定的γ/(Ω_c^2)以及OD下，能夠在雙光子共振點上最大化光譜訊號的Δc值，我們將這個Δc值稱為Δc_opt。我們發現Δc_opt有個臨界現象：在一個固定的γ/(Ω_c^2 )下，存在一個我們稱作OD_crit的OD臨界值；當OD≤OD_crit，Δc_opt就會是零，而當OD>OD_crit, Δc_opt不為零且隨著OD變大而變大。論文的第四章討論階梯型系統的四波混頻過程，並尋找能夠最大化輸出訊號的條件。

This thesis studies the respective Four-Wave Mixing (FWM) processes in a double-Λ system and in a diamond-type system. The first three chapters discuss the FWM process in a double-Λ system and focus on theoretically determining the conditions that maximize the probe output in the frequency domain at two-photon resonance. More specifically, we find the optimal Δc, or the coupling detuning, that maximizes the probe output at a fixed γ/(Ω_c^2) and OD at two-photon resonance. It turns out that there exists a critical value for OD, which we call OD_crit, such that the optimal Δc stays zero when OD≤OD_crit, and when OD>OD_crit, the optimal Δc is non-zero and increases as OD increases. The fourth and last chapter of the thesis turns to the FWM process in a diamond-type system and derives the condition that maximizes both the probe and the signal outputs.

Contents
Abstract    i
Contents    iii
Chapter 1.  Introduction    1
Chapter 2.  Background information on the Four-Wave Mixing (FWM) process in a double-Λ system    3
2.1　 Introducing the double-Λ four-level system    3
2.2　 Modeling the double-Λ four-level system    5
2.3   Steady-state solutions to the probe and signal fields    8
2.4   Revisiting the EIT system    11
Chapter 3.  Maximization and minimization of the ratio of the self-susceptibility term to the cross-susceptibility term in ρ_31    14
3.1　 Introduction and motivation: The unusual dip at the predicted peak positions in the probe spectrum    14
3.2　 Maximizing the ratio at two-photon resonance    18
3.2.1 General behavior of the ratio    18
3.2.2 Defining OD_crit and expressing OD_crit  as a function of β    20
3.2.3 Deriving Δc_opt, the optimal Δ_c that maximizes the ratio, as a function of OD and β for OD>OD_crit……………………………25
3.3   Minimizing the ratio for Δ_c≠0 cases    28
3.4   Minimizing the ratio for Δ_c=0 cases    34
Chapter 4.  Diamond-type FWM    38
4.1　 Introducing the diamond-type four-level system    38
4.2　 Optimizing the probe and signal outputs    41
Chapter 5.  Summary and Outlook    46
Bibliography    48
Appendix A    49
Appendix B    51
Appendix C    52

                                

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