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研究生： 羅佩凌
Luo, Pei-Ling
論文名稱： 氦原子單重態之精密光譜
Precision Spectroscopy of Singlet States in Atomic Helium
指導教授： 施宙聰
Shy, Jow-Tsong
口試委員: 倪簡白
汪治平
孔慶昌
王立邦
劉怡維
蔡錦俊
鄭王曜
周哲仲
學位類別： 博士
Doctor
系所名稱： 電機資訊學院 - 光電工程研究所
Institute of Photonics Technologies
論文出版年： 2014
畢業學年度： 102
語文別： 英文
論文頁數： 119
中文關鍵詞： 氦原子 、精密光譜 、絕對頻率
外文關鍵詞： Atomic helium, Precision spectroscopy, Absolute frequency
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    • 氦原子是最簡單的多電子原子，其電子能階可由QED (量子電動力學)的多體計算達到相當高的精確度。藉由實驗與理論的比較可以驗證原子理論的正確性，因此氦原子光譜之精密測量對於QED多體計算的發展佔有十分重要的地位。本論文主要是研究氦原子單重態能階躍遷之精密光譜，包括波長在2058 nm的21S0-21P1躍遷與波長在668 nm的21P1-31D2躍遷之精密光譜，我們也探討氦原子21S0-21P1-31D2能階之階梯式電磁誘導透明光譜。

    我們架設一台2.06 μm單頻且波長可調的Tm:Ho:YLF固態雷射，此雷射利用體積式布拉格光柵(VBG)作為波長選擇元件。當幫浦雷射功率達5 W時可得到200 mW的單模輸出，雷射頻率可以藉由改變VBG的溫度來做粗調，亦可用雷射共振腔上的PZT來微調，雷射單頻連續可調範圍可大於10 GHz。我們使用這台Tm:Ho:YLF固態雷射觀測二氧化碳分子在2.06 μm吸收光譜並進行雷射穩頻。當此雷射頻率鎖在二氧化碳分子躍遷譜線上時，頻率穩定度可達到3×10-9。

    氦原子21S0-21P1躍遷之精密光譜測量實驗中，我們同時使用兩台波長2058 nm的Tm:Ho:YLF固態雷射以及一台光纖式光頻梳來進行光譜測量。實驗測得的4He 21S0-21P1躍遷的絕對頻率為145622892886(183) kHz，其相對頻率不準度為1.3×10-9。利用4He 21S0-21P1躍遷的絕對頻率並結合其他精密量測的躍遷絕對頻率可以推得21P1能階之游離能，其準確度比過去測量高出一個數量級。此結果與目前最準確之理論值差約3.5σ，具有相當的重要性。我們也測量了3He-4He的同位素位移，其準確度亦比早期測量高出一個數量級。除了絕對頻率的測量，我們也詳細分析與討論不同實驗條件下的光譜形狀。

    氦原子21P1-31D2躍遷之精密光譜測量實驗中，我們使用一台頻率鎖在光纖光頻梳上之外腔式半導體雷射，其雷射波長為668 nm。實驗測得的4He 21P1-31D2躍遷的絕對頻率為448791399113(268) kHz，其相對頻率不準度為6×10-10。此結果之精確度比過去測量高出一個數量級。利用4He 21P1-31D2躍遷的絕對頻率並結合其他精密量測的躍遷絕對頻率可以推得21S0和21P1能階之游離能以及31D2 和 33D1的能階差。由此實驗我們再度確認21P1能階游離能理論計算與實驗測量值的不一致。

    最後，我們同時使用2058 nm雷射和668 nm雷射來測量氦原子21S0-21P1-31D2能階之階梯式電磁誘導透明光譜，此實驗可以得到小於自然線寬的光譜訊號。我們也討論不同實驗情況對於電磁誘導透明光譜訊號的影響。

    Helium is the simplest multi-electron atom and its electronic structure can be calculated very precisely by QED many-body calculations. Comparisons between experimental results and theoretical predictions therefore provide the best testing ground for atomic calculations and enable our better understanding of QED effects in bound systems. In this thesis, precision spectroscopy of the transitions in the helium singlet states including 21S0-21P1 transition at 2058 nm and 21P1-31D2 transition at 668 nm has been performed. Electromagnetically induced transparency (EIT) with a ladder-type system of the 21S0-21P1-31D2 transitions has also been studied.
    At first, a 2.06 μm tunable single-frequency volume Bragg grating (VBG)-based short-cavity Tm:Ho:YLF laser is constructed. The laser has hundreds of mW output power and a mode-hop free tuning range of 10 GHz. The frequency stabilization of this laser to a CO2 absorption line with a stability of 3×10-9 is achieved using frequency modulation and fluorescence detection.
    Precision spectroscopy measurements of the 21S0-21P1 transition at 2058 nm are performed using two Tm:Ho:YLF lasers and an Er:fiber-based optical frequency comb (OFC). This represents the first Doppler-free measurement on this transition. The absolute frequency of this transition in 4He is measured to be 145622892886(183) kHz with a relative uncertainty of 1.3×10-9. This result can be combined with other precisely measured transitions to derive the ionization energy of the 21P1 state with an uncertainty of approximately 200 kHz. The 3He-4He isotope shift of this transition is also determined to be 4248.7(5.3) MHz, 10 times more precise than previous measurement. Furthermore, the line shapes of the measured spectra are also studied.
    The frequency metrology of the 21P1-31D2 transition at 668 nm is performed using an OFC-stabilized external cavity diode laser (ECDL). The absolute frequency of this transition in 4He is measured to be 448791399113(268) kHz with a relative uncertainty of 6×10-10. This result combined with other precisely-known transitions enables us to derive the ionization energy of the 21P1 and the 21S0 states and the separation between the 31D2 and 33D1 states in 4He. By comparison with the theories, a serious discrepancy with the most precise atomic calculation is found on the ionization energy of the 21P1 state. This will stimulate more theoretical investigations on the singlet states of helium.
    In addition, the ladder-type EIT signal of the 21S0-21P1-31D2 transition is observed. The spectral width is reached to sub-natural linewidth. The EIT signals in different experimental conditions are also studied.

    摘要 i Abstract ii Acknowledgments iii Contents iv List of Figures vii List of Tables xx Chapter 1 Introduction 1.1 Energy Levels of Atomic Helium 1 1.2 Precision Measurement of Atomic Helium 3 1.2.1 Transition Frequency 3 1.2.2 Isotope Shift 8 1.2.3 Fine Structure Interval 10 1.3 Motivation 10 1.4 Thesis Outline 11 Chapter 2 Single Frequency Volume Bragg Grating-Based Short-Cavity Tm:Ho:YLF Laser at 2 μm 2.1 Diode-Pumped Tm:Ho:YLF Laser 13 2.2 Volume Bragg Grating (VBG) 14 2.3 Design and Property of the 2 μm Laser 16 Chapter 3 Frequency Stabilization of the Tm:Ho:YLF Laser to a CO2 Line at 2.06 μm 3.1 Observation of CO2 Fluorescence Signal 23 3.2 Frequency Stabilization 25 Chapter 4 Precision Spectroscopy of the 21S0-21P1 Transition in Atomic Helium at 2058 nm 4.1 Experimental Systems 28 4.1.1 Helium Discharge Cell 28 4.1.2 Acousto-Optic Modulator (AOM)-Based Laser Power Stabilizer 30 4.1.3 Fiber Optical Frequency Comb (OFC) 32 4.1.4 Frequency Offset Locking System of Laser and OFC 34 4.1.5 Tunable Frequency Offset Locking System of Two Lasers 36 4.2 Observation of Direct and Saturated Absorption Spectra of the 4He 21S0-21P1 Transition 38 4.2.1 Observation of Direct Absorption Spectrum 40 4.2.2 Observation of Saturated Absorption Spectrum 44 4.3 Absolute Frequency Measurement of the 21S0-21P1 Transition in 4He 55 4.4 Determination of the Ionization Energy of the 21P1 State in 4He 58 4.5 Isotope Shift between 3He and 4He 59 4.6 Saturated Absorption Line Shapes at Strong Absorption 61 4.6.1 Simulation of Saturated Absorption Spectroscopy 64 4.6.2 Saturated Absorption Spectrum of the 3He 21S0-21P1 Transition at Strong Absorption 69 Chapter 5 Absolute Frequency Measurement of the 21P1-31D2 Transition in 4He at 668 nm 5.1 Experimental Setup and Observation of Saturated Absorption Spectrum of the 4He 21P1-31D2 Transition 71 5.2 Absolute Frequency Measurement of the 21P1-31D2 Transition in 4He 76 5.3 Determination of the Ionization Energies of the 21S0 and 21P1 States and the Separation between the 31D2 and 33D1 States in 4He 78 5.4 Observation of Saturated Absorption Spectrum of the 3He 21P1-31D2 Transition 79 Chapter 6 Electromagnetically Induced Transparency in the 21S0-21P1-31D2 Transition in Atomic Helium 6.1 Introduction 82 6.1.1 Basic Principle 82 6.1.2 Ladder-Type EIT in an RF Discharge 84 6.2 Experimental Setup 86 6.3 Observation of EIT in the 4He 21S0-21P1-31D2 Transition 87 6.4 Observation of EIT in the 3He 21S0-21P1-31D2 Transition 92 Chapter 7 Conclusions and Future Works 7.1 Single Frequency VBG-Based Short-Cavity Tm:Ho:YLF Laser at 2 μm 94 7.2 Precision Spectroscopy of Atomic Helium 95 Appendix A Basic Model of Laser Absorption through a Cell 97 Appendix B Basic Model of Saturated Absorption 99 Appendix C Frequency Shift of the AOM-Based Amplitude Modulation Transfer Saturation Spectroscopy using Counter-Propagating Pump-Probe Configuration at Different Frequencies 102 C.1 Simulation 103 C.2 Experimental Observation 106 Appendix D Observation of the Saturated Absorption Spectra with Different Lock-in Phases 111 References 115

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