光子對與乙炔氣體的動態交互作用｜國立中央大學博碩士論文系統

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研究生：	潘冠廷 GUAN-TING PAN
論文名稱：	光子對與乙炔氣體的動態交互作用 Dynamic Interaction Behavior Between Photon Pairs AndAcetylene Gas
指導教授：	蔡秉儒 Pin-Ju Tsai
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 照明與顯示科技研究所 Graduate Institute of Lighting and Display Science
論文出版年：	2025
畢業學年度：	114
語文別：	英文
論文頁數：	150
中文關鍵詞：	乙炔、光子分子交互作用、快光、負群延遲、反常色散、吸收線
外文關鍵詞：	Acetylene, Interaction, fast light, absorption lines, negative group delays, anomalous dispersion
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我們研究了分子吸收與量子光傳播之間的交互作用，重點聚焦於單光子
層級下的快光（fast-light）現象。從量子觀點出發，我們推導了吸收
譜線的形成機制，並在符合因果律的條件下，模擬了由反常色散所引起
的脈衝前移效應。
在實驗方面，透過自發參數下轉換（SPDC）所產生的單光子脈衝，其頻
譜被調整至與乙炔分子的吸收線對齊，成功觀察到不違反因果律的可測
負群延遲（negative group delay）。
作為前置步驟，我們亦分析了 SPDC 雙光子訊號的訊噪比（SNR），以確
定最佳操作條件。此外，本研究也指出，快光效應可望藉由有效負折射
率提升光學陀螺儀的靈敏度。

We investigate the interaction between molecular absorption and quantum light
propagation, focusing on the fast-light phenomenon at the single-photon level.
From a quantum perspective, we derived the formation mechanism of absorption lines and simulated pulse advancement induced by anomalous dispersion
under causality. Experimentally, single-photon pulses generated via spontaneous parametric down conversion(SPDC) were spectrally aligned with an acetylene absorption line, enabling the observation of measurable negative group de
lays without violating causality. As a preparatory step, the signal-to-noise ratio (SNR) of SPDC biphotons was analyzed to determine the optimal operating
regime. The potential application of fast light in enhancing optical gyroscope
sensitivity via an effective negative refractive index is also highlighted.

Contents 
1 Introduction                          1 
1.1 Fast-Light Phenomenon ........................ 1 
1.2 Frequency Stabilization ......................... 2
2 Introduction and Theory Overview            3 
2.1 Introduction .....................................3
2.2 Field Quantization ...........................    3 
2.3 Gaussian State ..............................     7 
2.4 Coherent State ..............................     10 
2.5 Spontaneous Parametric Down-Conversion ............ 17 
3 Theory of Absorption Spectrum           29 
3.1 Introduction ...............................       29
3.2 Measurement-Device-Independent Quantum Key Distribution . . 29 
3.3 Two Level System ............................    38 
3.4 Doppler Broadening ..........................   46 
3.5 Beer–Lambert’s Law ..........................   50 
3.6 Kramers–Kronig Relations and Anomalous Dispersion ...51 
3.7 Simulation of Single-Photon Pulse Through Acetylene Absorption Cell .................................       56 
3.8 Mathematical Derivation of Pulse ................... 58 
3.9 Mathematical Derivation of Group Delay and Dispersion Effects.... 60 
3.9.1 Phase and Transmission Models ............... 60 
3.9.2 Derivation of Group Delay and Dispersion ......... 61  
3.9.3 Pulse Advancement and Centroid Shift ........... 61 
3.9.4 Illustration and Physical Interpretation .........62 
3.10 Simulation Result ............................ 63
3.10.1 Simulation Result With Different Bandwidth ......63 
3.10.2 Simulation Result With Different OD ............ 64 
4 Experiment                               69 
4.1 Introduction ............................... 69 
4.2 Absorption Spectrum Experiment .................. 70 
4.3 Characterization of Type-II SPDC Photon Source via Second-Order Correlation ................................ 73 
4.3.1 Photon Pair Generation via Type-II SPDC .......... 74 
4.3.2 Experimental Measurement of g_(s,h)^((2) ) .......74 
4.3.3 Theoretical Modeling of g_ ^((2) ) Degradation .....75 
4.3.4 Coincidence Timing and System Delay ........... 76 
4.3.5 Relevance to Quantum Illumination ............. 76 
4.4 Conclusion ............................... 77
4.5 Analysis of Single-Photon Pulse Through Acetylene Absorption Cell .................................... 78 
4.5.1 Experimental Verification ................... 86 
5 Conclusion     93 
A Frequency Stabilization by Absorption Spectra 95 
A.0.1 Error Signal Generation via Frequency Modulation .... 95 
A.0.2 lock-In Amplifier ........................ 101 
A.0.3 Simulate Result ......................... 103 
A.1 Experiment Result ........................... 107 
B Quantum-Enhanced Target Detection Using Time-Correlated Photon Pairs......113                    
                           vi
B.0.1 Performance Comparison: Quantum Illumination vs. Classical Coherent State ....................... 114 
B.1 Characterization of Type-II SPDC Photon Source via Second-Order Correlation and Its Application to Quantum Radar ......... 119 
B.1.1 Photon Pair Generation via Type-II SPDC .......... 119 
B.1.2 Measurement of g (2) s,h and Dependence on Pump Power . . 120 
B.1.3 Theoretical Model for g(2) Degradation ........... 121 
B.1.4 Application to Quantum Radar ................ 122 
C Gyroscopes Introduction   125 
C.1 The Sagnac Effect and Optical Gyroscopes .........126 
C.1.1 The Sagnac Effect ........................ 126
C.1.2 Role and Operating Principle of Optical Gyroscopes .... 127 
C.1.3 Frequency Splitting and Fast-Light Effect in Resonant Cavities ................................ 128 
Bibliography 131
                               vii
                                

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