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研究生: 黃耀欽
Huang, Yao-Chin
論文名稱: 鋰原子低能階的雷射光譜
Laser Spectroscopy of Low-lying Levels in Atomic Lithium
指導教授: 王立邦
Wang, Li-Bang
口試委員: 周哲仲
Chou, Che-Chung
鄭王曜
Cheng, Wang-Yau
劉怡維
Liu, Yi-Wei
褚志崧
Chuu, Chih-Sung
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: 2018
畢業學年度: 106
語文別: 英文
論文頁數: 176
中文關鍵詞: 鋰原子超精細結構外腔式雷射精密光譜紫光鐳射
外文關鍵詞: Lithium, Hyperfine Splitting, ECDL, Spectroscopy, UV Laser
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  • 本論文研究鋰原子低能階的雷射光譜。實驗上,我們分別建立兩套相似的雷射系統,其中一套雷射系統為光譜雷射,其頻率穩定在共焦的法布立-培若(Fabry-Pérot)腔體上,藉由改變腔體長度達到掃描雷射的頻率功能並且可得到鋰原子光譜。另一套雷射系統為參考雷射,此雷射的頻率會鎖在碘分子躍遷譜線。利用光電倍增管偵測雷射誘發的螢光訊號,並且記錄兩套雷射系統之間頻率的差值。

    在2P_{1/2}超精細結構分裂及D1同位素偏移實驗上,我們釐清了不同的團隊量測結果的爭議。結論上,鋰-6與鋰-7的第一激發態2P_{1/2}超精細結構分裂分別為26.108(9)百萬赫玆和91.873(5)百萬赫玆與目前的理論計算相符。而同位素偏移大小為10533.800(15)百萬赫玆,結合實驗測量與理論計算的同位素偏移也可計算出鋰-7與鋰-6相對均方根核電荷半徑的大小差值為-0.720(6)費米平方。

    為了要檢測理論計算在鋰原子低能階的準確度,我們也測量激發態3P_{1/2}的超精細結構分裂。實驗精準度相較以往的測量提高六點七倍,此外,在決定絕對頻率數值精確度提高三千倍。


    This dissertation studies the low-lying levels of ^{6,7}Li in a well-collimated atomic beam. We have built two laser systems, one of which frequency is stabilized on a confocal Fabry-Perot cavity and scans the lithium spectrum by tuning the cavity length as a spectroscopy laser. Another laser is locked to molecular iodine transition near lithium resonance line as a reference laser. The laser-induced fluorescence signal is detected by a photomultiplier, and
    the beat frequency between the spectroscopy laser and the reference laser is recorded.

    We have clari ed that the 2P_{1/2} hyperfi ne structure splitting and D1 isotope shift for stable ^{6,7}Li disagree with previous experiments. The 2P_{1/2} hyper fine interval are 26.108(9) MHz and 91.873(5) MHz for ^{6}Li and ^{7}Li, respectively. The D1 isotope shift is 10533.800(15) MHz. Combining the measured D1 isotope shift with the calculated energy shift determines the relative squared nuclear charge radius to be -0.720(6) fm^{2}.

    In order to test atomic calculations in other low-lying levels, we have also measured the hyperfi ne splitting of 3P_{1/2} state. Our result improves the precision by a factor of 6.7 compared to previous measurements. Furthermore, the absolute frequency is measured and the precision is three thousand times better than previous results.

    Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .ii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .xi 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.1 The Importance of Li D Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.2 Nuclear Theory Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.1.3 The Discrepancies of Li D1 Line and Splitting Isotope Shift . . . . . . . 4 1.1.4 Study of 3P Level in Lithium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2 Overview of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2 Lithium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1 Lithium Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.2 Energy Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 Hyper ne Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.2 Hyper ne Anomaly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 2.3 Isotope Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.1 Mass Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2 Field Shift (Volume Shift) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.4 Absolute Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3 External Cavity Diode Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 3.2 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.3 External Cavity on Littrow Con figuration . . . . . . . . . . . . . . . . . . . . . . 31 3.3.1 Grating Parameter in Littrow-type Cavity . . . . . . . . . . . . . . . . . . . . 31 3.3.2 Laser Linewidth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.3.3 Lasing Mode Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3.3.4 Mode-hop Free Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.4 ECDL Design and Assembly . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4.1 Laser Diode Tube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.4.2 Grating and Mount . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.4.3 Peltier Cooler Module . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.4 Protect Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.5 Modulation Circuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 3.4.6 Finished Product Picture and Items List . . . . . . . . . . . . . . . . . . . . . . 42 4 Iodine Spectroscopy for 647 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4.1 Laser Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 4.2 Iodine Spectroscopy near 646.7 nm Region . . . . . . . . . . . . . . . . . . . . 48 4.3 Iodine Experiment System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.3.1 Absorption Spectrum and Sub-Doppler Spectrum . . . . . . . . . . . . . . 50 4.3.2 Dispersion-like Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 4.4 Pressure versus Temperature of Iodine Cell . . . . . . . . . . . . . . . . . . . . 53 4.5 Absolute Frequency Measurement System . . . . . . . . . . . . . . . . . . . . . 55 4.6 Absolute Frequency Measurement Result . . . . . . . . . . . . . . . . . . . . . . 60 4.6.1 System Stabilization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.6.2 Pressure Shift Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 4.6.3 The a1, a10, and a15 Components Result . . . . . . . . . . . . . . . . . . . . 64 4.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5 Second Harmonic Generation Ultraviolet Light at 323 nm . . . . . . . . . . . 67 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 5.2 Phase Matching Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.2.1 Critical Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 5.3 Walk-o ff Angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 5.4 E ffective Nonlinear Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 5.5 Boyd-Kleinmann Theory: Optimum Beam Waist . . . . . . . . . . . . . . . . . 74 5.6 Cavity Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 5.6.1 A Stable Optical Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5.6.2 Enhancement Pw with a Bow-tie Cavity . . . . . . . . . . . . . . . . . . . . . . 85 5.6.3 Second Harmonic Power P2w . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 6 Measurement of Hyperfi ne Intervals and Isotope Shift for 2S1/2-2P1/2(D1 line) . .91 6.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 6.2 Energy Level Diagram of 2S1/2-2P1/2 . . . . . . . . . . . . . . . . . . . . . . . . 93 6.3 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.3.1 Laser System for spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.3.2 Atomic Beam and Vacuum System . . . . . . . . . . . . . . . . . . . . . . . . . . 97 6.3.3 Reference Laser System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 6.4 Result - (New Reference System) . . . . . . . . . . . . . . . . . . . . . . . . . . . 102 6.4.1 Noise and Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 6.4.2 Laser Power Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 6.4.3 The Hyperfi ne Splitting of 2P1/2 . . . . . . . . . . . . . . . . . . . . . . . . . 107 6.4.4 D1 Isotope Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 6.4.5 Absolute Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.5 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.5.1 Hyperfi ne Splitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 6.5.2 D1 Isotope Shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.5.3 Absolute Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.6 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 7 Measurement of Hyperfi ne Intervals for 2S1/2-3P1/2 . . . . . . . . . . . . 125 7.1 Background of the 3P State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 7.2 Characterization of the Lasers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.2.1 Fundamental Laser of 647 nm . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 7.2.2 Optical Path . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 7.2.3 SHG Cavity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 7.3 The 3P State Transition Signal Search . . . . . . . . . . . . . . . . . . . . . . . 135 7.4 3P1/2 State Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 7.4.1 Line Profi le Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 7.4.2 Hyper fine Splitting of 3P1/2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 7.4.3 Absolute Frequency Determination . . . . . . . . . . . . . . . . . . . . . . . . 143 7.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 Appendix A Monolithic Cvity Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 B Tapered Amplifi er Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 C Matlab Program for Calculation of Optimal Beam Waist . . . . . . . . . . . . .155 D SHG Cavity Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

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