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系統識別號 U0026-0408201612521000
論文名稱(中文) 量子絕熱捷徑之比較與分析
論文名稱(英文) Comparsion and Analysis of Shortcuts to Adiabaticity
校院名稱 成功大學
系所名稱(中) 光電科學與工程學系
系所名稱(英) Department of Photonics
學年度 104
學期 2
出版年 105
研究生(中文) 林智中
研究生(英文) Chih-Chung Lin
學號 L76031273
學位類別 碩士
語文別 英文
論文頁數 87頁
口試委員 指導教授-曾碩彥
口試委員-魏明達
口試委員-徐旭政
中文關鍵字 能量轉換  絕熱系統  絕熱捷徑  微擾理論 
英文關鍵字 population transition  adiabatic transition  shortcuts to adiabaticity  perturbation theory 
學科別分類
中文摘要 在能量轉換的過程,已經被提出許多的方法,但是那麼多種方法,什麼時候應該使用什麼方法會比較好我們無從得知,在考慮不同的情況下,選擇適合的方法,讓以後的人在設計波導時能夠更加容易。首先,本論文介紹的第一種方法,主要是改良絕熱捷徑的分析,一般的絕熱系統下,要達到能量轉換必須得花很長時間,絕熱捷徑能夠將時間縮短,但卻會使得結果不夠穩定,因此我們使用的第一種方法主要是利用絕熱捷徑接近於絕熱系統,使得可以解決時間問題以及結果不穩定的狀況;第二種方法,主要是利用微擾理論探討,當我們已知有特定微擾下,可以直接將其優化,微擾理論在不同階數下精確度會不一樣,在此篇論文我們將討論到7階狀態。最終將此兩種方式的參數設計成相同型式,並且相互比較,判斷出在特定的情況下選擇較適合的優化方式。
英文摘要 The population transition have a lot of method be proposed. However, how should we choose the method in different situation we don’t know. In order to let design of waveguide easier, we want to select suitable methods under distinct circumstances. In this thesis, we will introduce two different methods, optimization of adiabaticity and robustness quantum control, respectively. The common shortcut to adiabaticity(STA) can improve long time problem of adiabatic transition, but the robustness is worse. And the first method not only can improve this problem but also can improve the robustness by approaching trajectory of adiabatic. The second method major is use the perturbation theory to improve particular perturbation. We compare distinct methods in the same parameters that we can know which method is better in different situation. Let the users can choose whichever particular method they want.
論文目次 中文摘要 i
Abstract ii
致謝 iii
Table of Contents iv
List of Figures vi
Chapter 1 Introduction 1
1.1 Introduction 1
1.1.1 Adiabaticity 2
1.1.2 Shortcuts to adiabatic with Lewis-Riesenfeld invariant 3
1.1.3 Optimization of adiabaticity 4
1.1.4 Robust quantum control 5
1.2 Organization of the Thesis 6
Chapter 2 Theoretical Analysis 7
2.1 Two-level System: Rabi Oscillation 7
2.2 Lewis-Riesenfeld invariant protocol 16
2.3 Bloch sphere 20
2.4 Instantaneous and invariant eigenstates 23
2.5 Optimization of adiabaticity by using shortcut to adiabaticity 26
2.6 Robust Quantum Control by a single-shot shaped pulse 28
Chapter 3 Simulation Results and Discussion 34
3.1 Schematic of the Parameters used for Simulator 35
3.2 Robustness with respect to Rabi-frequency (Ω) compare with optimization of adiabaticity 37
3.2.1 Third-order 38
3.2.2 Fifth-order 45
3.2.3 Seventh-order 52
3.3 Another robustness compare with optimization of adiabaticity 59
3.3.1 Robustness with respect to detuning (Δ) compare with optimization of adiabaticity 60
3.3.2 Robustness with respect to Rabi-frequency (Ω) by another global phase term. 67
3.3.3 Robustness with respect to both Rabi-frequency (Ω) and detuning (Δ) compare with optimization of adiabaticity 75
Chapter 4 Conclusion and Perspectives 83
4.1 Conclusion 83
4.2 Perspectives 85
Reference 86
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