摘要
本論文主要是以電磁感應透明(electromagnetically induced transparency)的
方式量測出與宇稱不守恆相關的參數(χ)，以及利用原子束的特性，觀測亞都普
勒光譜中的粒子數相干布居數囚禁(coherent population trapping)效應以及粒子
數的分布。在鉈的熱原子腔體中，首先利用光纖耦合的相位調製器產生一高一
低的頻率帶，使得我們可以在短時間內測量1283奈米中相距21千兆赫茲的兩道
躍遷的信號，大幅縮小環境以及系統因素所產生的不確定性，再利用535奈米躍
遷中顯著的同位素位移來區別鉈-205和其同位素鉈-203的效應，這使我們能夠直
接量測出鉈-205和鉈-203分別的χ值，實驗結果也達到了1%的精準度，並與其中
一組理論值相符，為長久以來的宇稱不守恆量測提供一項支持。
原子束的架設則作為下一步來量測鉈的量子干涉效應，由於鉈原子的熔點
高且蒸氣壓偏低，使得原子束必須在高溫下才能產生至可觀測的量。在本論文
中，我們利用許多不銹鋼的毛細管作為噴嘴，來實現高濃度低發散角的原子
束。並利用自製的環形共振腔體將鈦藍寶石雷射的頻率從755奈米提升至377.5奈
米，以符合鉈原子的躍遷頻率。在原子束中，我們利用兩組光電倍增管來觀測
鉈的螢光，並藉由原子束所具有的時序關係推論出鉈原子在量子干涉下的螢光
光譜以及粒子數在能階上的分布情形，最後清楚解析出反應過程中完整的動態
變化。

Abstract
This paper mainly measures the parity non-conservation (PNC) related pa-
rameter, χ, with the method of electromagnetically induced transparency (EIT),
and uses the characteristics of thallium atomic beams to observe the coherent
population trapping (CPT) and population distribution under the sub-Doppler
spectroscopy. In the thermal atomic cavity of thallium, a fiber-coupled phase
modulator is used to generate a high frequency sideband and a low frequency
sideband, so we can measure the signals of two 1283 nm transitions with 21 GHz
frequency gap in a short time, substantially reducing the uncertainties arising from
environmental and systemic factors. Besides, using the property of significant iso-
topic shift in the 535 nm transition, we can distinguish the effects of thallium-205
and its isotope thallium-203. This advantage allows us to directly measure the
χ values of thallium-205 and thallium-203, respectively. The experimental result
has also reached an accuracy of 1%, and the χ value is consistent with one of the
theoretical calculations. We provide a support for the long dispute on the atomic
thallium PNC measurements.
The setup of the atomic beam is the next step to measure the quantum inter-
ference effect of thallium. Due to the high melting point and low vapor pressure
of thallium atoms, the thallium vapor must be generated at a relatively high tem-
perature to produce an observable atomic beam. In this paper, we use many
stainless steel capillaries as nozzles to achieve high concentration and low diver-
gence angle of the atomic beam. Additionally, the frequency of the Ti:sapphire
laser is increased from 755 nm to 377.5 nm by using a homemade ring resonant
cavity to match the thallium transition. In the atomic beam, we use two sets
of photomultipliers (PMT) to observe the fluorescence of thallium, and deduce
the fluorescence spectrum under the quantum interference. We can also infer the
population distribution after the quantum interference by the time sequence re-
lationship of the atomic beam. Finally, the completely dynamic variation in the
interaction is clearly analyzed.

Contents
Abstract (Chinese) I
Acknowledgements (Chinese) II
Abstract III
Contents V
List of Figures X
List of Tables XV
1 Introduction 1
1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Atomic Parity Non-Conservation . . . . . . . . . . . . . . . . . . . 2
1.2.1 NSI part . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2.2 NSD part . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Successful Atomic PNC methods . . . . . . . . . . . . . . . . . . . 5
1.4 Discrepancy between The Two Groups in Tl PNC Measurements . 6
1.5 Improvement of the PNC Optical Rotation Experiment . . . . . . . 8
2 Facts about Thallium 12
2.1 Three major transitions and energy states for the experiments . . . 12
2.2 Thallium isotopic characteristic . . . . . . . . . . . . . . . . . . . . 14
2.3 Hyperfine structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.4 Doppler width and spectrum estimation . . . . . . . . . . . . . . . 16
2.5 population and vapor pressure . . . . . . . . . . . . . . . . . . . . . 16
3 Experiment Apparatus 19
3.1 Laser structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.1 377 nm laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.2 535 nm laser . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.3 1283 nm laser . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Laser and Cavity stabilization . . . . . . . . . . . . . . . . . . . . . 28
3.2.1 Laser stabilization . . . . . . . . . . . . . . . . . . . . . . . 28
3.2.2 Cavity stabilization . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 Cell vapour system . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 PPLN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Second Harmonic Generation UV Light at 377 nm 41
4.1 Ti:sapphire laser . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4.2 Non-linear crystal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
4.3 Phase matching conditions . . . . . . . . . . . . . . . . . . . . . . . 46
4.3.1 Coherence length . . . . . . . . . . . . . . . . . . . . . . . . 47
4.3.2 Birefringent optical crystal . . . . . . . . . . . . . . . . . . . 47
4.3.3 Critical phase matching . . . . . . . . . . . . . . . . . . . . 49
4.3.4 Effective non-linear coefficient . . . . . . . . . . . . . . . . . 51
4.4 Anti-reflective coating and Brewster’s angle . . . . . . . . . . . . . 52
4.4.1 Anti-reflective coating . . . . . . . . . . . . . . . . . . . . . 53
4.4.2 Brewster’s angle . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.5 Walk-off angle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4.6 Ring cavity design for doubling the laser frequency . . . . . . . . . 60
4.6.1 Cavity configurations . . . . . . . . . . . . . . . . . . . . . . 60
4.6.2 Beam waist for the tangential and sagittal plane . . . . . . . 63
4.7 Resonant enhancement . . . . . . . . . . . . . . . . . . . . . . . . . 66
4.7.1 Impedance matching . . . . . . . . . . . . . . . . . . . . . . 66
4.8 TEM00 coupling method . . . . . . . . . . . . . . . . . . . . . . . . 68
5 High-Sensitivity Sideband Amplitude Modulation Spectroscopy 70
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.2 Sideband Amplitude Modulation . . . . . . . . . . . . . . . . . . . 72
5.3 Experiment Setup for Measuring CH4 Absorption . . . . . . . . . . 75
5.4 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6 Transitions with Single Photon Absorption 83
6.1 Single photon direct absorption spectroscopy . . . . . . . . . . . . . 83
6.1.1 Beer–Lambert Law . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.2 Natural linewidth . . . . . . . . . . . . . . . . . . . . . . . . 84
6.1.3 Lorentzian profile . . . . . . . . . . . . . . . . . . . . . . . . 86
6.1.4 Gaussian profile . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.1.5 Comparison between Lorentzian and Gaussian line profiles . 89
6.1.6 Voigt profile . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.2 Single photon absorption for thallium . . . . . . . . . . . . . . . . . 90
6.2.1 1283 nm E1-forbidden transition . . . . . . . . . . . . . . . 91
6.2.2 535 nm E1-allowed transition . . . . . . . . . . . . . . . . . 91
6.2.3 377 nm E1-allowed transition . . . . . . . . . . . . . . . . . 94
7 Electric Quadrupole Amplitude Experiment with Electromagnet-
ically Induced Transparency 96
7.1 Electromagnetically Induced Transparency . . . . . . . . . . . . . . 97
7.1.1 EIT compared to direct absorption . . . . . . . . . . . . . . 98
7.1.2 Typical three-level EIT model . . . . . . . . . . . . . . . . . 99
7.1.3 EIT in thallium forbidden transition . . . . . . . . . . . . . 103
7.1.4 Fiber-EOM Frequency Bridging . . . . . . . . . . . . . . . . 105
7.2 Experiment for measuring the χ value . . . . . . . . . . . . . . . . . 107
7.3 EIT spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
7.4 Systematic effects and error budget . . . . . . . . . . . . . . . . . . 114
7.4.1 Light power effect . . . . . . . . . . . . . . . . . . . . . . . . 114
7.4.2 Number density . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.4.3 Error budget . . . . . . . . . . . . . . . . . . . . . . . . . . 116
7.5 Result and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . 120
7.5.1 χ value for 205Tl and 203Tl . . . . . . . . . . . . . . . . . . . 120
7.5.2 Connection between χ and thallium PNC . . . . . . . . . . . 121
8 Thallium Atomic Beam 123
8.1 Atomic Beam Structure . . . . . . . . . . . . . . . . . . . . . . . . 123
8.2 Heater . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
8.3 Observation from the photomultiplier . . . . . . . . . . . . . . . . . 128
9 Coherent Population Trapping Observation by the Thallium Atomic
Beam 132
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
9.1.1 Baryon asymmetry . . . . . . . . . . . . . . . . . . . . . . . 132
9.1.2 Charge conjugation, Parity, and Time reversal symmetry . . 133
9.1.3 Electric dipole moments . . . . . . . . . . . . . . . . . . . . 133
9.1.4 CPT model . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
9.2 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
9.2.1 Atomic beam structure . . . . . . . . . . . . . . . . . . . . . 137
9.2.2 Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
9.3 Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
9.3.1 Time-averaged measurement: CPT spectroscopy . . . . . . . 141
9.3.2 Transient measurement: CPT dynamics . . . . . . . . . . . 142
9.3.3 Frequency-dependent dynamics . . . . . . . . . . . . . . . . 149
9.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Bibliography 153

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