基於電磁誘發透明的量子薛丁格方程式模擬器

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姓名

邵詳崴(Siang-Wei Shao) 查詢紙本館藏

畢業系所

物理學系

論文名稱

基於電磁誘發透明的量子薛丁格方程式模擬器
(Quantum Schrödinger Equation Simulator based on Electromagnetically Induced Transparency)

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至系統瀏覽論文 (2027-7-31以後開放)

摘要(中)

本研究主要目的是探討如何使用光來模擬帶電粒子在電磁場中的運
動。我所使用的方法是電磁誘發透明(EIT)，通過調控EIT系統中的各
項參數，例如耦合光以及雙光子失諧，即可為EIT中的暗態極化子合成
相應的人造規範場。進而讓系統成為一個可以計算薛丁格方程式的模擬
器。在此研究中，我使用了此EIT薛丁格方程式模擬器模擬了幾個不同
的電磁場環境，分別是等效靜磁場下的朗道能階(Landaulevel)，等效靜
電場下的量子諧振子(Quantum Harmonic Oscillation) 以及使用等效時
變電場來展示受激拉曼絕熱通道(STIRAP)。附錄則是介紹我研究中所
使用到的數值方法等。

摘要(英)

This study explores the use of light to simulate the motion of charged particles in electromagnetic fields, employing Electromagnetically Induced Transparency (EIT). By manipulating parameters within the EIT system, such as coupling light and two-photon detuning, synthetic electromagnetic fields can be generated for dark-state polaritons, let the system become a quantum Schrödinger equation simulator. We utilize this EIT Schrödinger equation simulator to mimic various eletromagnetic field environments, including Landau levels under an effective magnetic field, quantum harmonic oscillation under an effective static electric field, and using an effective time
varing electric field to demonstrate STIRAP. The appendix details numerical methods employed in this study.

關鍵字(中)

★ 電磁誘發透明
★ 人造規範場

關鍵字(英)

論文目次

摘要vii
Abstract ix
誌謝xi
目錄xiii
圖目錄xv
使用符號與定義xix
一、第一章緒論1
1.1 EIT系統.................................................................. 1
1.2靜止脈衝.................................................................. 3
1.3人造規範場............................................................... 5
1.4受激拉曼絕熱通道(STIRAP)........................................ 7
二、第二章理論模型9
2.1一維EIT系統........................................................... 9
2.2二維EIT系統........................................................... 15
2.3量子薛丁格方程式模擬器............................................. 17
2.4朗道能階.................................................................. 21
xvii
目錄
三、第三章模擬分析25
3.1朗道能階.................................................................. 25
3.1.1 EIT的朗道能階................................................ 27
3.1.2二維EIT在人造規範勢的尺度效應....................... 29
3.1.3 EIT在朗道能階中的邊界態................................. 31
3.2量子諧振子............................................................... 34
3.3 EIT系統的STIRAP................................................... 37
3.3.1系統位能......................................................... 37
3.3.2能階躍遷......................................................... 38
四、第四章結論41
參考文獻43
附錄A附錄47
A.1數值模擬方法............................................................ 47
A.2漩渦計算範圍............................................................ 48
A.3設計障礙區............................................................... 48

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指導教授

廖文德(Wen-Te Liao)

審核日期

2024-7-30

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