本論文中，我們使用自製的外腔二極體雷射 ( ECDL ) 當作種子光源，其波長為 778 奈米，經由一個 Newport 製造的錐形放大器 ( Tapered amplifier ) 放大其功率後，我們可以得到超過 500 毫瓦的功率；我們把一部分的光打進一個波導式週期性極化的鈮酸鋰 ( waveguide PPLN ) ，將 778 奈米雷射光倍頻產生將近 2 毫瓦的 389 奈米光源，然後用此光源進行氦原子三重態 2S → 3P 的飽和吸收光譜；同時另一部份的光源和我們實驗室的光頻梳 ( optical frequency comb ) 系統做拍頻，再利用偏差式鎖頻 ( offset lock ) 的線路將我們的雷射鎖在光頻梳上，外腔二極體雷射頻率的穩定度可到達 1.3 × 10^(−11)，因此我們可以精確地量測雷射及譜線躍遷的絕對頻率。
　　絕對頻率測量結果如下： 2^(3)S_(1) → 3^(3)P_(2) 的中心頻率是 770 724 067.399(161) 百萬赫茲，2^(3) S_(1) → 3^(3)P_(1) 的中心頻率是 770 724 726.246(180) 百萬赫茲，準確度可以達到 2.3 × 10^(−10)；同時 3^(3)P_(2) 與 3^(3)P_(1) 的精細結構分裂量測結果為 ν_(12) = 658.847(45) 百萬赫茲，這個結果與理論值及其他團隊測量的結果互相符合。

In this thesis, we used a home-made external cavity diode laser (ECDL) at 778 nm to seed a commercial tapered amplifier (Newport TA-7600), which can boost the laser power up to more than 500 mW. After the tapered amplifier, the laser beam was split into two beams. One was sent to a waveguide PPLN to double the frequency of 778 nm and the other one was referenced to an optical fiber comb system in our lab. We used the beam of 2 mW at 389 nm to perform saturated absorption spectroscopy and measured the helium 2^(3)S to 3^(3)P transition. The absolute frequency was measured by the Erbium-doped fiber frequency comb. We used the beat frequency between the ECDL and fiber comb system and an offset lock circuit to lock our laser on fiber comb system. The frequency stabilization of the ECDL can reach 1.3 × 10^(−11). Therefore, we can be precisely measured the absolute frequency of our laser and the targeted transition.
　　The results of the transition frequencies were as follow : 2^(3)S_(1) → 3^(3)P_(2) f = 770 724 067.399(161) MHz and 2^(3) S_(1) → 3^(3)P_(1) f = 770 724 726.246(180) MHz, The precision of the results reached 2.3 × 10^(−10), The fine structure splitting between 3^(3)P_(2) and 3^(3)P_(1) states was also measured, and ν_(12) = 658.847(45) MHz,which is in agreement with theoretical calculation.

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . iii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . .vii

1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
　1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
　1.2 Previous Studies of Heilum 2^(3)S → 3^(3)P Transition . . . . . 1
　　1.2.1 Previous Studies In Other Group . . . . . . . . . . . . . . 1
　　1.2.2 Previous Studies In Our Group . . . . . . . . . . . . . . . 3
　　1.2.3 Some Problems for Previous Work . . . . . . . . . . . . . . 5

2 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . 9
　2.1 External Cavity Diode Laser (ECDL) . . . . . . . . . . . . . . .10
　2.2 Frequency Stabilization . . . . . . . . . . . . . . . . . . . .13
　2.3 Optical Fiber Comb (OFC) System . . . . . . . . . . . . . . . .15
　　2.3.1 Brief History . . . . . . . . . . . . . . . . . . . . . . .15
　　2.3.2 Experimental Setup of Optical Fiber Comb (OFC) . . . . . . .16
　　2.3.3 Frequency Stabilization of OFC . . . . . . . . . . . . . . .17
　　2.3.4 Frequency Accuracy of OFC . . . . . . . . . . . . . . . . .17
　2.4 Absolute Frequency Measurement System . . . . . . . . . . . . .19
　　2.4.1 Beat Frequency with OFC . . . . . . . . . . . . . . . . . .19
　　2.4.2 Offset Lock Circuit . . . . . . . . . . . . . . . . . . . . .21

3 Second Harmonic Generation Near Ultraviolet Light at 389 nm . . . .23
　3.1 Bismuth Triborate (BiBO) Crystal . . . . . . . . . . . . . . . .23
　3.2 Periodically Poled Potassium Titanyl Phosphate (PPKTP) Crysta. .26
　3.3 Periodically Poled Lithium Niobate (PPLN) with Waveguide Type. .29
　3.4 Compare All Ways to Generate 389 nm Light . . . . . . . . . . .32

4 Saturated Absorption Spectroscopy for Helium at 389 nm . . . . . . .33
　4.1 Saturated Absorption Spectroscopy . . . . . . . . . . . . . . .34
　4.2 Helium Discharge Cell . . . . . . . . . . . . . . . . . . . . .36
　4.3 Acousto-Optical Modulators (AOM) . . . . . . . . . . . . . . . .37
　4.4 Absolute Frequency Determination . . . . . . . . . . . . . . . .39

5 Data Analysis and Results . . . . . . . . . . . . . . . . . . . . .41
　5.1 Measured Line Shapes . . . . . . . . . . . . . . . . . . . . . .41
　　5.1.1 Velocity Changing Collisions . . . . . . . . . . . . . . . .43
　　5.1.2 Light-Pressure-Induced Frequency Shifts. . . . . . . . . . .45
　　5.1.3 Laser Power Normalization . . . . . . . . . . . . . . . . .49
　5.2 Center Frequencies . . . . . . . . . . . . . . . . . . . . . . .51
　　5.2.1 Pressure Shift . . . . . . . . . . . . . . . . . . . . . . .53
　　5.2.2 Laser Power Shift and RF Discharge Power Shift . . . . . . .54
　5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . .55
　　5.3.1 Uncertainty Budget . . . . . . . . . . . . . . . . . . . . .55
　　5.3.2 Fine Structure Splitting Between 3^(3)P_(1)and 3^(3)P_(2)
　　　　　States. . . . . . . . . . . . . . . . . . . . . . . . . . . .55
　　5.3.3 Final Center Frequencies and Fine Structure Splitting
　　　　　Values. . . . . . . . . . . . . . . . . . . . . . . . . . . .56

6 Conclusion and Future Works . . . . . . . . . . . . . . . . . . . .59
　6.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . .59
　6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . .60

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .64
　A Energy level diagram of 3He . . . . . . . . . . . . . . . . . . .65
　B Circuit diagrams . . . . . . . . . . . . . . . . . . . . . . . . .67

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