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系統識別號 U0026-0907202009564600
論文名稱(中文) 馬約拉納零能模與馬約拉納量子比特之非馬可夫退相干動力學
論文名稱(英文) Non-Markovian decoherence dynamics of Majorana zero modes and Majorana qubits
校院名稱 成功大學
系所名稱(中) 物理學系
系所名稱(英) Department of Physics
學年度 108
學期 2
出版年 109
研究生(中文) 黎瀚林
研究生(英文) Hon-Lam Lai
學號 L28031083
學位類別 博士
語文別 英文
論文頁數 101頁
口試委員 指導教授-張為民
口試委員-周宗憲
口試委員-陳岳男
口試委員-梁永成
口試委員-張亞中
召集委員-李定國
中文關鍵字 拓撲量子計算  馬約拉納零能模  退相干 
英文關鍵字 topological quantum computation  Majorana zero mode  decoherence 
學科別分類
中文摘要 在這篇論文中,我們使用嚴格主方程去研究馬約拉納零能模裡的退相干動力學,我們採用的Kitaev模型是一個一維的p波非自旋拓撲超導縺,並置於操控閘引起的電荷擾動中。我們的嚴格主方程的推導方式是應用Feynman-Vernon影響泛函於包含超導耦合的費米子開放系統。在這個嚴格主方程的架構中,我們可以詳細地描述馬約拉納零能模在局域擾動下的非馬可夫動力學。我們接著研究拓撲超導縺中的馬約拉納量子比特在辮子操作下的退相干動力學,其中的辮子操作是透過控制拓撲超導縺的化學能和耦合實現的。透過嚴格計算出馬約拉納量子比特的動力學,我們展現了其量子相干性是如何藉著交換馬約拉納零能模而產生的。我們同時使用嚴格主方程指出馬約拉納零能模是如何因著操控閘的電荷擾動在零溫度和有限溫度的情形中耗散。
英文摘要 In this thesis, We use the exact master equation approach to investigate the decoherence dynamics of Majorana zero modes in the Kitaev model, a 1D p-wave spinless topological superconducting chain (TSC), that is disturbed by gate-induced charge fluctuations. The exact master equation is derived by extending Feynman-Vernon influenced functional technique to fermionic open systems involving pairing excitations. We obtain the exact master equation for the zero-energy Bogoliubov quasiparticle (bogoliubon) in the TSC, and then transfer it into the master equation for the Majorana zero modes. Within this exact master equation formalism, we can describe in detail the non-Markovian decoherence dynamics of the zero-energy bogoliubon as well as Majorana zero modes under local perturbations. We also study the decoherence dynamics of Majorana qubit braiding operations in a TSC system, in which the braiding is performed by controlling the electron-chemical potentials of the TSCs and the couplings between them. By solving rigorously the Majorana qubit dynamics, we show how the Majorana qubit coherence is generated through bogoliubon correlations formed by exchanging Majorana zero modes between two TSCs in braiding operations. We also demonstrate with the exact master equation how Majorana zero modes and also the bogoliubon correlations dissipate due to charge fluctuations of the controlling gates at both the zero and finite temperatures.
論文目次 Chapter 1 Introduction......1
Chapter 2 Majorana zero modes and Majorana quits......7
Chapter 3 Decoherence theories of Majorana zero modes......13
Chapter 4 Decoherence dynamics of Majorana zero modes under charge fluctuations......27
Chapter 5 Decoherence dynamics of Majorana qubits under braiding operations......50
Chapter 6 Conclusion and future works......69
References......71
Appendix A......77
Appendix B......79
Appendix C......92
Appendix D......99
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