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研究生： 張君毅
Chang, Chun-Yi
論文名稱： 量測同調態的維格納函數
Measurement of Wigner function of coherent state
指導教授： 陳泳帆
Chen, Yong-Fan
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： 2017
畢業學年度： 105
語文別： 中文
論文頁數： 50
中文關鍵詞： 維格納函數 、平衡零差偵測 、量子態斷層掃描
外文關鍵詞： Wigner function, Balanced homodyne detection, Quantum state tomography
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    • 我們建立一套維格納函數(Wigner function)的量子態斷層掃描(Quantum State Tomography, QST)實驗量測系統。不同於使用壓電陶瓷(Piezoelectric Ceramic Transducer, PZT)的平衡零差偵測(Balanced Homodyne Detection, BHD)系統，我們使用電光相位調製器(Electro-Optic Phase Modulator, EPM)來改變干涉儀中局域振盪光(Local-Oscillator light, LO)與訊號光(signal light)的相對相位。但是遇到許多超出預期的問題，例如目前的訊噪比不高，以及相位的不穩定等，使我們目前所量測到對光子同調態的維格納函數失真很嚴重。最後，我們針對問題提出了一些改善的方法及未來的展望。

    We build a quantum state tomography system for measuring Wigner function. We apply an electro-optic phase modulator (EPM) to modulate the relative phase between the signal light and the local-oscillator light (LO) in the interferometer, which is different from using a piezoelectric ceramic transducer (PZT) in the balanced homodyne detection (BHD). Suffering from many unexpected problems such as low signal-to-noise ratio and the instability of phase in our system, our measurements of Wigner function of coherent state are distorted seriously. Finally, we propose some improvements against the problems and outlooks.

    摘要 i 英文延伸摘要 ii 誌謝 vii 目錄 viii 表格 x 圖片 xi 第1章 緒論 1 1.1 介紹. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 實驗動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 第2章 基本理論 3 2.1 維格納函數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.1.1 密度算符(density operator) . . . . . . . . . . . . . . . . . . . . . . 3 2.1.2 特徵函數(characteristic function) . . . . . . . . . . . . . . . . . . 4 2.1.3 維格納函數(Wigner function) . . . . . . . . . . . . . . . . . . . . 5 2.1.4 同調態的維格納函數. . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 分光鏡(Beam Splitter, BS) . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 平衡零差偵測(Balanced Homodyne Detection, BHD) . . . . . . . . . . . 12 2.4 量子態斷層掃描(Quantum State Tomography, QST) . . . . . . . . . . . . 14 第3章 實驗系統與架設 20 3.1 實驗架設. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.2 電光相位調制器. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 實驗參數. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.4 實驗方法. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 第4章 結果與討論 32 4.1 實驗結果. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2 結果與討論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 第5章 結論與未來展望 42 5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 5.2 未來展望. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 參考文獻 44

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