離子囚禁是量子計算最有前景的平台之一。它具有較長的相干時間和極高的量子邏輯門保真度。此外，離子囚禁系統還可用於多種應用，如量子感測、精密測量和量子模擬等。為了探索這些熱門的研究課題，我們在清華大學建立了一個離子阱系統。在這篇論文中，我將介紹離子阱系統和實驗進展。這篇論文主要在介紹離子阱系統以及電磁波引發的透明光譜光譜。在第二章中，論文會提及離子阱囚禁原理和離子與光的交互作用。第三章則會提到離子阱的硬體架構，包括金屬電極、射頻共振腔、真空系統和雷射系統，並討論設計參數和整個系統的架構。在第四章中，論文會討論如何收集囚禁單離子螢光、成像以及離子的微運動對光譜造成的影響，並提供方法補償微運動。第五章則會討論EIT光譜方面的內容，包括理論計算和實驗擬合。首先會帶入簡單的三能階系統進行計算，然後對八能階的EIT光譜進行理論計算，後會透過光譜擬合磁場的大小。最後討論溫度對光譜的影響，期望未來可以透過光譜量測系統溫度。在最後一章中，論文會作出總結並展望未來的工作方向。

Trapped ions are one of the most promising platforms for quantum comput-ing. They have long coherence times and extremely high-fidelity quantum logicgates. In addition, trapped ion systems can be used in various applications, such asquantum sensing, precision measurements, and quantum simulations. In order toexplore these exciting research topics, we have built an ion trap system at NTHU.This thesis focuses on introducing the ion trap system and electromagneti-cally induced transparency spectroscopy. Chapter 2 discusses the principles ofion trapping and the interaction between ions and light. Chapter 3 discusses thehardware configuration of the ion trap, including metal electrodes, RF resonator,vacuum systems, and laser systems. We also explain the design parameters and theoverall architecture of the system. In Chapter 4, we discuss how to collect singleion fluorescence, imaging, and the effects of ion micromotion on the spectrum,and provide methods for compensation of micromotion. Chapter 5 discusses theEIT spectrum, including EIT theoretical calculations and experimental fits. First,we will introduce a simple three-level system and calculate the EIT spectrum ofan eight-level system. We will fit the magnitude of the magnetic field throughspectrum. Finally, we will discuss the effect of temperature on the spectrum andhope to measure the temperature of the system through this model in the future. Inthe final chapter, we will make a summary and look forward to future work.

1引論......1
2離子陷阱理論和離子與光的交互作用......3
2.1離子陷阱囚禁原理. . . . . 3
2.1.1離子陷阱的簡諧位能近似 . . . . . 9
2.2鈣離子的能階與雷射冷卻......10
2.2.1鈣原子介紹及鈣原子光離子化......10
2.2.2鈣離子的能階......12
2.2.3鈣離子的都卜勒冷卻(Doppler cooling)......13
2.3離子和光的基礎交互作用......14
3離子阱的實驗架設......16
3.1真空系統......17
3.2離子陷阱設計與模擬......19
3.2.1離子阱模擬......20
3.3射頻共振腔(Helical resonator)設計及直流電極......22
3.3.1螺旋射頻共振腔......24
3.3.2直流電壓源......28
3.4囚禁離子螢光成像系統......29
3.4.1光電倍增管(Photomultiplier tube, PMT)探測......29
3.4.2 CCD成像系統......30
3.5雷射系統......32
3.5.1自製外腔雷射（external cavity diode laser, ECDL)......33
3.5.2光路架設......33
4單離子囚禁......35
4.1囚禁單離子製備......35
4.2單離子的囚禁頻率測定......38
4.2.1單離子的間距測定......39
4.3單離子微運動校正......41
4.4磁場校正......44
5單離子非線性光譜量測......46
5.1電磁感應透明光譜理論計算......46
5.1.1簡單三能階系統......46
5.1.2塞曼分裂(zeeman splitting)八能階系統......50
5.2 EIT實驗結果......58
5.2.1無磁場簡單EIT光譜......58
5.2.2塞曼分裂能階EIT光譜......58
5.3溫度修正的EIT譜線......62
6總結與展望......63
附錄......64
Simion模擬軟體操作......64
林德布拉德方程(Lindblad equation)計算......68
偶極躍遷矩陣強度修正與林德布拉德方程去相干項計算......70
文獻......75

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