本論文分為兩部分：其一，以 Red Pitaya STEMlab 平台與 Linien 軟體實現對外腔式二極體雷射鎖頻，取代傳統龐雜之鎖頻架構，並可使用圖形使用者介面輕鬆鎖在無都普勒飽和吸收光譜內任意峰值之頻率。30 分鐘漂移量測顯示多數時段的頻率飄移獲得有效抑制；有效線寬約 3.77 MHz，小於飽和吸收譜線寬量級，為後續實驗提供良好條件。
其二，利用電磁誘發透明現象量測銫原子D2線之超精細結構，透過在室溫銫蒸氣中實作 V 型電磁感應透明（V-EIT）。聚焦探測光經鎖頻後固定於 |6S1/2, F=3> 到 |6P3/2, F=2> 以及 |6S1/2, F=3> 到 |6P3/2, F=3> 兩種情況；耦合光則在 |6S1/2, F=3> 到 |6P3/2, F=2,3,4> 之間掃頻，並以無都卜勒飽和吸收光譜作為頻率校正參照。
室溫下，實驗訊號受原子速度群影響，產生比預期更多的穿透峰光譜。透過建立以都卜勒速度類別為基礎之模型，將耦合光的頻率失諧對應到原子速度群，成功預測穿透峰位置與相對峰值，並初步解釋峰值大小的成因；結果與實驗訊號相符。
在功率相依性量測中，固定探測功率為 5 μW 與 10 μW，改變耦合光束的功率 Pc，透過 Voigt 擬合分析多峰訊號各自的線寬和相對振幅。結果顯示，線寬幾乎不隨 Pc 變化，而相對振幅則隨 Pc 呈非線性增長，且與不同頻率之躍遷強度相關，這與光泵浦實驗中觀察到的行為一致。

This thesis comprises two parts. First, using the Red Pitaya STEMlab 125–14 platform together with the Linien software, we implement frequency locking of an external-cavity diode laser (ECDL), replacing a conventional, more complex locking setup. Via a graphical user interface, the laser can be locked to any peak in the Doppler-free saturated-absorption spectrum (DFSAS). A 30-minute drift test shows that frequency wander is effectively suppressed for most intervals; the effective linewidth is about 3.77 MHz, smaller than the saturated-absorption linewidth scale and sufficient for the subsequent experiments.
Second, we measure the hyperfine structure of the Cs D2 line via electromagnetically induced transparency by implementing V-type EIT in room-temperature Cs vapor. The focused, frequency-locked probe was fixed at |6S1/2, F = 3> → |6P3/2, F = 2> and |6S1/2, F = 3> → |6P3/2, F = 3>, while the coupling beam scans across |6S1/2, F = 3> → |6P3/2, F = 2, 3, 4>. The Doppler-free saturated-absorption spectrum was used as the frequency correction reference.
At room temperature, velocity-group effects generate more transparency peaks than initially expected. Using a Doppler velocity-group model that maps the coupling detuning to the addressed velocity groups, we predict the peak positions and relative amplitudes and give a preliminary account of their magnitudes; the results are consistent with the measurements.
In the power dependence measurements, with the probe power fixed at 5 and 10 μW, we varied the coupling power Pc and, using Voigt fits, analyzed the linewidth and relative amplitude of multiple peaks. The results show that the linewidth is nearly independent of Pc, whereas the peak amplitudes increase nonlinearly with Pc and correlate with transition strength, consistent with optical pumping.

[1] Daniel A. Steck. Cesium d line data. Technical report, Oregon Center for Optics and Department of Physics, University of Oregon, 2025.
[2] Stephen E. Harris. Lasers without inversion: Interference of lifetime-broadened resonances. Physical Review Letters, 62(9):1033–1036, 1989.
[3] Klaus-Jochen Boller, Atac Imamoglu, and Stephen E. Harris. Observation of electromagnetically induced transparency. Physical Review Letters, 66(20):2593–2596, 1991.
[4] Stephen E. Harris and Lene Vestergaard Hau. Nonlinear optics at low light levels. Physical Review Letters, 82(23):4611–4614, 1999.
[5] Lene Vestergaard Hau, Stephen E. Harris, Zachary Dutton, and Cyrus H. Behroozi. Light speed reduction to 17 metres per second in an ultracold atomic gas. Nature, 397(6720):594–598, 1999.
[6] Mauro Paternostro, Myungshik S. Kim, and Byoung S. Ham. Generation of entangled coherent states via cross-phase modulation in a double electromagnetically induced transparency regime. Physical Review A, 67(2):023811, 2003.
[7] Marlan O. Scully and M. Suhail Zubairy. Quantum Optics. Cambridge University Press, 1997.
[8] Claude Cohen-Tannoudji, Jacques Dupont-Roc, and Gilbert Grynberg. Atom–Photon Interactions: Basic Processes and Applications. Wiley, New York, 1st edition, 1992.
[9] Benjamin R. Mollow. Power spectrum of light scattered by two-level systems. Physical Review, 188(5):1969–1975, 1969.
[10] Thi Thuy Nguyen. Multi-photon processes in the atomic system of cesium. Doctoral dissertation, National Cheng Kung University, Department of Physics, Tainan, Taiwan, 2022.
[11] Sacher Lasertechnik Group. Lynx Tunable Littrow External Cavity Diode Laser: User’s Manual. Rudolf Breitscheid Straße 1–5, 35037 Marburg, Germany, 3 edition, 2006.
[12] Christopher J. Foot. Atomic Physics. Oxford University Press, Oxford, UK, 1st edition, 2005.
[13] Prosenjit Majumder, Hemant Yadav, Rakesh Tirupathi, Kamalkant, Shruti Jain, Poonam Yadav, Arnab Ghosh, Apoorav Singh Deo, and Deepshikha Singh. Advancing frequency locking: Modified fpga-guided direct modulation spectroscopy for laser stabilization. Optics and Laser Technology, 170:110247, 2024.
[14] Benjamin Wiegand, Bastian Leykauf, Robert Jördens, and Markus Krutzik. Linien: A versatile, user-friendly, open-source fpga-based tool for frequency stabilization and spectroscopy parameter optimization. Review of Scientific Instruments, 93(6):063001, 2022.
[15] Red Pitaya Team. Linien user-friendly locking of lasers using red pitaya (stemlab 125-14) that works every time, 2024.
[16] John M. Supplee, Edward A. Whittaker, and Wilfried Lenth. Theoretical description of frequency modulation and wavelength modulation spectroscopy. Applied Optics, 33(27):6294–6302, 1994.
[17] Bristol Instruments, Inc. Model 671 Laser Wavelength Meter: User’s Manual. Victor, NY, USA, 2016.
[18] Sheng-Ta Lin. Theoretical simulation of electromagnetically induced transparency in cs atom d2 line. Master’s thesis, National Cheng Kung University, Department of Physics, Tainan, Taiwan, 2025.