鋰原子2S→3S雙光子躍遷的頻率量測｜國立清華大學博碩士論文庫

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研究生：	許家祥 Chia-Hsiang Hsu
論文名稱：	鋰原子2S→3S雙光子躍遷的頻率量測 Frequency measurement of 2S→3S two-photon transition of atomic lithium
指導教授：	劉怡維 Yi-Wei Liu
口試委員:
學位類別：	碩士 Master
系所名稱：	理學院 - 物理學系 Department of Physics
論文出版年：	2005
畢業學年度：	93
語文別：	英文
論文頁數：	45
中文關鍵詞：	雙光子躍遷、無都卜勒效應譜線、飛秒光頻梳、同位素位移、鋰原子
外文關鍵詞：	two-photon transition, Doppler-free spectroscopy, optical femtosecond comb, isotope shift, lithium atom
相關次數：	點閱：2 下載：0
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本實驗利用波長735奈米的固態鈦藍寶石雷射觀察鋰原子2S1/2-3S1/2雙光子躍遷螢光光譜，並使用飛秒光頻梳系統做絕對頻率測量，目的與基本原子理論做比較，理論包括相對論、量子電動力學(QED)與原子核結構之計算。
鋰原子產生方法為在真空腔內的加熱爐加熱產生鋰原子束，並與雷射光垂直交會，雷射光經凹面鏡反射，形成兩道方向相反的光束以達到雙光子躍遷。雷射光功率為450 mW，產生之螢光訊號 (2P → 2S) 由光電倍增管所偵測並經過鎖相放大器解調。由於雙光子的無都卜勒增寬效應下，譜線線寬為 10 MHz。共四條超精細譜線被觀察到，包括兩個同位素7Li和6Li，其躍遷絕對頻率由飛秒光頻梳系統測量達精確度280 kHz。飛秒光頻梳系統由一鎖模鈦藍寶石雷射所產生，其準確度可達 10-11。四條譜線中最強的訊號為 F=2→F=2 (7Li)，其訊雜比達100，絕對頻率為407808975.87(13) MHz，同位素位移為11454.95(51) MHz。此結果可用來測試理論的正確性，與理論計算(包含相對論與量子電動力學的計算)比較結果相符並且精確度提昇一個數量級。由絕對頻率與能階結構可計算出3S能階之超精細結構常數，由於同位素位移與同位素之質量、原子核半徑有關，因此推算7Li與6Li原子核半徑平方差為1.2(3) fm2。此結果與其他實驗做比較，其中躍遷頻率有3 MHz的差距，推測主要由雷射系統頻率不穩定造成頻率計數器之誤差。

Lithium 2S1/2 → 3S1/2 transition has been observed by high-precision laser spectroscopy using two-photon Doppler-free excitation and fluorescence detection. The two-photon excitation is performed in a weakly collimated atomic beam using a titanium-sapphire (TIS) ring laser at 735 nm with 450 mW laser power. Four transition lines, including isotopes 6Li and 7Li, were observed and the linewidth is 10
MHz and SNR of the strongest line is ~100. Absolute frequencies of all hyperfine components have been measured to an uncertainty of 280 kHz using optical femtosecond comb. The resulting frequency of 7Li : F = 2→2 is 407808975.87(13) MHz and isotope shift is 11454.95(51) MHz. There are discrepancies with recent work, and this may be due to laser instability in our system. The results are compared with the theoretical works, including relativistic and QED energy contributions, and the accuracy is improved by an order of magnitude. Combined with theory, the squared
nuclear radii difference between 6Li and 7Li is 1.2(3) fm2.

Introduction
1 Lithium and fundamental atomic physics  . . . . . . . . . . . . . 1
1.1 Precision physics of simple atoms . . . . . . . . . . . . . . . 1
1.2 Interests in lithium property . . . . . . . . . . . . . . . . . 2
2 Atomic theory calculations . . . . . . . . . . . . . .  . . . . . 3
2.1 Nonrelativistic wave functions  . . . . . . . . . . . . . . . . 4
2.2 Relativistic correction . . . . . . . . . . . . . . . . . . . . 6
2.3 Quantum electrodynamic corrections  . . . . . . . . . . . . . . 7
2.4 Nuclear size correction . . . . . . . . . . . . . . . . . . . . 8
2.5 Transition energy and isotope shifts  . . . . . . . . . . . . . 9
3 Doppler-free two-photon transition . . . . . . . . . . . . . . . 10
3.1 Multiphotonic transitions  . . . . . . . . . . . . . . . . . . 11
3.2 Two-photon transition probability  . . . . . . . . . . . . . . 11
3.3 Two-photon absorption lineshape  . . . . . . . . . . . . . . . 13
3.4 Light shifts (ac Stark eRect)  . . . . . . . . . . . . . . . . 15
4 Optical femtosecond comb based on Mode-locked Ti:sapphire laser. 16
4.1 Mode-locked Ti:sapphire laser  . . . . . . . . . . . . . . . . 17
4.2 Supercontinuum generation  . . . . . . . . . . . . . . . . . . 18

Experiment
1 Atomic structure of lithium  . . . . . . . . . . . . . . . . . . 21
1.1 Lithium property . . . . . . . . . . . . . . . . . . . . . . . 21
1.2 Energy level diagram . . . . . . . . . . . . . . . . . . . . . 23
2 Review of 2S→3S two-photon spectroscopy . . . . . . . . . . . . 23
3 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . 24
3.1 Laser system . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Atomic lithium beam  . . . . . . . . . . . . . . . . . . . . . 25
3.3 Fluorescence detection . . . . . . . . . . . . . . . . . . . . 25
4 Absolute frequency measurement . . . . . . . . . . . . . . . . . 26
4.1 Femtosecond comb system  . . . . . . . . . . . . . . . . . . . 26
4.2 Repetition rate and oRset frequency stabilization  . . . . . . 26
4.3 Femtosecond comb test  . . . . . . . . . . . . . . . . . . . . 27
4.4 Beat measurement . . . . . . . . . . . . . . . . . . . . . . . 27
Results and discussions
1 Results  . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2 Systematic eRect . . . . . . . . . . . . . . . . . . . . . . . . 36
2.1 Doppler background . . . . . . . . . . . . . . . . . . . . . . 36
2.2 Light shift  . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.3 Second-order Doppler shift . . . . . . . . . . . . . . . . . . 38
3 Hyperfine constant, isotope shift, and nuclear size  . . . . . . 39
4 Discussions  . . . . . . . . . . . . . . . . . . . . . . . . . . 41

Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

                                

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