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研究生: 林昇達
Lin, Sheng-Ta
論文名稱: 銫原子D2線電磁誘導透明現象之理論模型與模擬
Theoretical Simulation of Electromagnetically Induced Transparency in Cs Atom D2 Line
指導教授: 蔡錦俊
Tsai, Chin-Chun
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: 2025
畢業學年度: 114
語文別: 英文
論文頁數: 126
中文關鍵詞: 電磁誘導透明光學布洛赫方程V型系統銫-133光學幫浦光譜擬合
外文關鍵詞: Electromagnetically induced transparency, optical Bloch equations, V-type system, Cesium-133, optical pumping, spectral fitting
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  • 電磁誘導透明(EIT)是一種量子干涉效應:當兩個相干光場同時驅動三能階原子時,原本的吸收譜線中會出現狹窄的透射窗。本論文針對室溫銫-133(D2 線)之 V 型 EIT,在「非弱探測」條件下建立穩態密度矩陣模型,以擬合實驗量得之線寬約 30--50MHz 的光譜。模型首先考慮都卜勒展寬與速率平均:不同速度族群對探測與耦合光之等效失諧不同,可能同時滿足通往不同激發超精細能階的兩光子共振,形成速度選擇式共振;經速度平均後,整體光譜可出現多個峰。接著將雷射等效線寬及原子間碰撞等效應納入鬆弛項(弛豫矩陣),並使各參數與實驗可量測量(光斑尺寸、光功率 -> 拉比頻率、原子樣本溫度與偏振)對應。
    在此基礎上,進一步加入對應π與σ+-偏振的光學幫浦效應,以描述塞曼次能階居量的穩態重分佈。此模型能合理再現整體線形與主要線寬尺度,並在相對峰值對比上顯著改善,尤其於σ+-偏振配置下表現更佳。隨後,亦納入次級光學幫浦效應之修正:部分通道因居量重新分布而導致探測光吸收增強的現象。最終結果顯示,加入此修正後可有效減少模擬與實驗間的殘差,進一步提升擬合一致性與參數可辨識度。

    Electromagnetically induced transparency (EIT) is a quantum-interference effect in which a narrow transmission window appears inside an absorption line when two coherent optical fields simultaneously drive a three-level atom. In this thesis, a steady-state density-matrix model is developed for V-type EIT in room-temperature Cs-133 vapor on the D2 line under non-weak-probe conditions to fit the measured spectra with linewidths of 30--50MHz. The model first incorporates Doppler broadening and velocity averaging: atoms with different velocities experience different effective detunings for the probe and coupling fields, allowing simultaneous two-photon resonances to different excited-state hyperfine levels and forming velocity-selective resonances. After averaging, multiple peaks appear in the overall spectrum. The effective laser linewidth and collisional relaxation are then included in the relaxation matrix, with all parameters linked to measurable quantities (beam size, optical power -> Rabi frequency, cell temperature, and polarization).
    Based on this framework, optical pumping (OP) effects for π and σ+- polarizations are further incorporated to describe the steady-state redistribution of Zeeman-sublevel populations. The model successfully reproduces the overall lineshape and main linewidth scale and significantly improves the relative peak contrasts, particularly for σ+--polarized configurations. Subsequently, secondary optical pumping effects are also introduced: certain channels exhibit enhanced probe absorption due to population redistribution. The final results show that incorporating these corrections effectively reduces the residual differences between simulation and experiment, further improving the consistency of spectral fitting and the identifiability of physical parameters.

    摘要 I Abstract II Acknowledgements IV Contents VII List of Tables X List of Figures XI Chapter 1 Introduction 1 1.1 Electromagnetically Induced Transparency (EIT) 1 1.2 Brief View of Cesium D2 Hyperfine and Multi-level 4 Chapter 2 Theory 5 2.1 Density Matrix Approach and Optical Bloch Equation 5 2.1.1 Density Matrix Approach 5 2.1.2 Optical Bloch Equation 7 2.2 Intensity Relation of Light-atom Interaction 7 2.3 Two-level System 11 2.3.1 Hamiltonian 12 2.3.2 Doppler Effect 22 2.4 Three-level System 25 2.4.1 Λ-type System 26 2.4.2 V-type System 32 2.4.3 Doppler Effect 37 2.5 Optical Pumping Effect 39 2.6 Simulation Setup 42 2.6.1 Cesium D2 Hyperfine Structure 42 2.6.2 Rabi Frequency 43 Chapter 3 Simulation Result 45 3.1 Two-level System 45 3.1.1 Population 45 3.1.2 Absorption Coefficient 47 3.1.3 Intensity 49 3.1.4 Doppler Broadening Effect 51 3.2 Three-level System: Λ-type 55 3.2.1 Doppler Effect 60 3.3 Three-level System: V-type 61 3.3.1 Doppler Effect 65 3.4 Experiment Fitting 66 Chapter 4 Conclusion 84 References 85 Appendix A Simulation Codes in Wolfram Mathematica 88 A.1 Two-level System 88 A.2 Λ-type System 90 A.3 V-type System 91 A.4 Rabi Frequency & C-G Coefficient 92 A.5 Optical Pumping 93 A.6 Fitting 96

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