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研究生：	許濬璿 Shiu, Jiun-Shiuan
論文名稱：	原子系綜中可訂製的光子對生成：多功能量子資訊應用平台 Tailored Photon Pair Generation in Atomic Ensembles: A Versatile Platform for Quantum Information Applications
指導教授：	陳泳帆 Chen, Yong-Fan
學位類別：	博士 Doctor
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：	113
語文別：	英文
論文頁數：	397
中文關鍵詞：	雙光子生成、原子系綜、DLCZ 協定、雷射冷卻原子、自發四波混頻
外文關鍵詞：	Biphoton generation, Atomic ensembles, DLCZ protocol, Laser-cooled atoms, Spontaneous four-wave mixing
ORCID：	https://orcid.org/0009-0006-6585-2062
相關次數：	點閱：23 下載：14
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本論文針對原子系統中可調控的雙光子生成進行了完整的實驗與理論研究，涵蓋了自發四波混頻 (spontaneous four-wave mixing, SFWM) 以及 Duan-Lukin-Cirac-Zoller (DLCZ) 型自發拉曼散射 (spontaneous Raman scattering, SRS) 兩種方案。在SFWM 機制中，兩個雷射場同時與原子系統交互作用，驅動四光子散射過程，並藉由集體原子效應產生具時間相關性的光子對。我們系統性地分析了光子配對比 (即區分同調的成對光子與非同調的背景光子)，並提出一種方法可從實驗數據中提取該比值。結果顯示，光子配對比隨光學厚度 (OD) 增加而上升，在 OD = 120 時達到 0.89，此時每秒可產生 1.16 × 10^7 對有關連性的光子，總產生率率則為 1.30 × 10^7。在低增益區域中，所產生的雙光子具有高純度，訊雜比高達 241，超越古典極限五個數量級。此外，雙光子的頻寬與頻率皆可調控，使其能高效耦合至窄頻量子系統。相比之下，DLCZ 型方案則依賴於序列式拉曼過程：首先由單一激發脈衝誘發自發拉曼散射，產生 Stokes 光子並在原子系統中建立基態同調性；隨後延遲施加的耦合場再將此同調性轉換為 anti-Stokes 光子。此機制可實現精確的時間控制，並支援具需求式的雙光子產生。雖然其效率與SFWM 同樣隨 OD 增加而提升，但由於基礎物理機制不同，所展現的量子關聯性亦有差異。我們同時提出了首個可以捕捉 DLCZ 型雙光子生成動力學的開放系統理論模型，並由此獲得新的物理洞見。綜合而言，本研究建立了一個多功能的量子光源平台，具備應用於量子通訊、量子記憶與量子運算的潛力。

This thesis presents a comprehensive experimental and theoretical study of tailored biphoton generation in atomic ensembles, utilizing both spontaneous four-wave mixing (SFWM) and Duan-Lukin-Cirac-Zoller (DLCZ)-type spontaneous Raman scattering schemes. In SFWM, two laser fields interact simultaneously with the ensemble to drive a four-photon scattering process, generating time-correlated photon pairs through collective atomic interactions. We systematically analyze the photon pairing ratio—distinguishing coherent pairs from incoherent background photons—and develop a method to extract this ratio from experimental data. The pairing ratio increases with optical depth (OD), reaching 0.89 at OD = 120, where 1.16 × 10^7 correlated pairs per second are produced from a total rate of 1.30 × 10^7. In the low-gain regime, the biphotons exhibit high purity, with a signal-to-background ratio of 241, surpassing the classical limit by five orders of magnitude. Additionally, the biphoton bandwidth and frequency are tunable, enabling efficient coupling to narrowband quantum systems. In contrast, the DLCZ-type scheme relies on a sequential Raman process: a single excitation pulse induces spontaneous Raman scattering, emitting a Stokes photon while establishing ground-state coherence in the ensemble. A delayed coupling field then retrieves this coherence as an anti-Stokes photon. This mechanism enables precise temporal control and supports on-demand photon pair generation. While its efficiency shows similar OD dependence as SFWM, the underlying physical processes result in different quantum correlations. We also present the first open-system theoretical model capturing the dynamics of DLCZ-type biphoton generation, providing new insights. Together, these results establish a versatile platform for quantum communication, memory, and computation.

摘要i
Abstract ii
Acknowledgements iii
Table of Contents v
List of Tables ix
List of Figures x
Chapter 1. Introduction 1
Chapter 2. Theory I: Interaction between Atoms and Classical Fields 4
1 Atom–Field Interaction 4
2 Investigation of Two-Level Atom–Field Interaction via Schrödinger Equation 7
3 Density Matrix Expression 11
4 Rabi Oscillation 13
4.1. Application 1: Ramsey Interferometry 17
4.2. Application 2: Quantum Zeno Effect 19
5 Relaxation Processes and Optical Bloch Equation 21
6 Damped Rabi Oscillation 24
7 Maxwell–Schrödinger Equation 26
8 Absorption Spectrum 29
9 Perturbation Theory 33
10 Propagating Dynamics 37
10.1. Fourier Analysis 38
10.2. Laplace Analysis 40
11 Coherent Population Trapping 42
11.1. Basis Transformation 42
11.2. Coherent Population Trapping: Resonant Scenario 44
11.3. Coherent Population Trapping: Non-Resonant Scenario 47
12 Λ-Type Electromagnetically Induced Transparency 48
12.1. Slow Light Effect 51
12.2. Physical Mechanism Behind Transparency 53
12.3. Dark-State Polariton 55
12.4. Light Storage 58
13 Autler–Townes Effect 60
A Complex Integral 62
Chapter 3. Theory II: Interaction between Atoms and Quantum Fields 66
1 Field Quantization 66
1.1. Mode Expansion in a Cavity 67
1.2. Plane-Wave Representation and Quantization 69
2 Photon Statistics 71
2.1. Quadrature Variance 73
2.2. Coherent State 75
2.3. Squeezed State 80
2.4. Thermal State 83
3 Collective Atomic Operator Framework 86
4 Atomic Dynamics 87
4.1. Single-Mode Bosonic System Coupled to a Reservoir 87
4.2. Green’s Function Method 90
4.3. Preservation of Commutation Relations 91
4.4. Heisenberg–Langevin Equation and Fluctuation–Dissipation Theorem 92
4.5. Single-Mode Fermionic System Coupled to Reservoir 94
4.6. Two-Level Atom Coupled to Bosonic Reservoir 95
5 Continuous-Variable Commutation Relations 100
6 Maxwell–Schrödinger Equations for Quantized Fields 102
7 A Two-Level Atom Ensemble Perturbed by a Quantized Field 103
8 Dark-State Polariton 107
9 Raman Transition 109
A Diffusion Coefficients and Fluctuation–Dissipation Theorem 115
Chapter 4. Laser-Cooled Atomic Ensemble: Preparation and Configuration 117
1 Diode Laser and External Cavity Diode Laser 117
1.1. Diode Laser 118
1.2. External-Cavity Diode Laser 120
1.3. Tapered Amplifier 121
2 Frequency Stabilization System 124
2.1. Saturated Absorption Spectroscopy 124
2.2. Lock-in Amplifier 125
2.3. Integrator 127
2.4. Fabry–Pérot Interferometer 129
3 Rubidium Atom 131
4 Electro-Optic Modulator 133
5 Acousto-Optic Modulator 135
6 Magneto-Optical Trap 139
7 Vacuum System 144
8 Beam Size and Rabi Frequency 146
9 Experiment of Electromagnetically Induced Transparency 149
A Thermal Doppler Broadening 153
B Polarization Basis: From Classical Waves to Quantum States 154
Chapter 5. Spontaneous Four-Wave Mixing: Theory 158
1 Biphoton Generation 159
1.1. Heisenberg–Langevin Operator Approach 160
1.2. Derivation of Field Operators 165
1.3. Photon Generation Rate 168
2 Biphoton Spectrum 172
3 Correlation Functions 188
3.1. Second-Order Autocorrelation Function 188
3.2. Second-Order Cross-Correlation Function 197
3.3. Conditional Autocorrelation Function 207
4 Wave-Function-Based Method 212
4.1. Linear and Nonlinear Susceptibilities 215
4.2. Characteristic Times 216
A Analytical Formulation of SFWM 217
B Thermal-State Distribution of Biphotons 220
Chapter 6. Spontaneous Four-Wave Mixing: Experiment 223
1 Energy Level Selection and State Preparation 223
2 Experimental Setup 227
2.1. Guiding Method 229
2.2. Etalon Filter 232
2.3. Single-Photon Counting Module 237
2.4. Time-of-Flight Multiscaler 240
3 Coincidence Counts and Coincidence Count Rate 243
3.1. Coincidence Count Representation 243
3.2. Coincidence Count Rate Representation 245
3.3. Reverse Heralding Configuration 246
4 Experimental Results and Discussion 248
4.1. Bandwidth-Controllable Biphotons 249
4.2. High-Purity Biphotons 252
4.3. Highly Correlated Ultrabright Biphotons 254
4.4. Frequency-Tunable Biphotons 256
4.5. Asymmetrically Generated Biphotons 262
A User Interface of the TOF Software 269
Chapter 7. DLCZ-Type Spontaneous Raman Scattering: Theory 272
1 The Write Process 273
1.1. Numerical Illustration of Analytical Results 280
1.2. Ground-State Approximation 290
1.3. Large-Detuning Approximation 301
1.4. Creation of Spinwave Coherence 308
1.5. Raman Polariton 317
2 The Read Process 321
2.1. Discussion of Computational Results 326
2.2. Rapid Retrieval 333
2.3. Adiabatic Retrieval 335
3 Correlation Functions 337
3.1. Second-Order Autocorrelation Function 337
3.2. Second-Order Cross-Correlation Function 339
A Derivation of Zeroth-Order Dynamic 343
B Magnus Expansion 346
Chapter 8. DLCZ-Type Spontaneous Raman Scattering: Experiment 350
1 Ensemble Preparation and Experimental Setup 350
2 Cross-Correlation Measurement 352
3 Experimental Results and Discussion 355
Chapter 9. Conclusion 361
References 363
                                    

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