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系統識別號 U0026-0401201311014700
論文名稱(中文) 雙光子過程的非馬可夫動力學
論文名稱(英文) Non-Markovian Dynamics of Two-Photon Processes
校院名稱 成功大學
系所名稱(中) 物理學系碩博士班
系所名稱(英) Department of Physics
學年度 101
學期 1
出版年 102
研究生(中文) 柯博仁
研究生(英文) Bo-Ren Ke
學號 L26991017
學位類別 碩士
語文別 英文
論文頁數 42頁
口試委員 指導教授-張為民
口試委員-周忠憲
口試委員-張志義
中文關鍵字 空腔  雙光子過程  非馬可夫動力學  主方程 
英文關鍵字 Cavity  Two-photon processes  non-Markovian dynamics  master equation 
學科別分類
中文摘要 本論文中,我們研究空腔同時藉由光子吸收/放射與雙光子過程耦合到一個熱庫的非馬可夫動力學。藉由結合海森堡運動方程法與主方程法,我們可以得到空腔的主方程。此主方程可幫助我們分析一些重要的物理量例如空腔的電場、光子數。此空腔系統與熱庫間的雙光子過程將會引起一個感應的雙光子耦合並且只有在弱耦合下此效應才可被忽略。此效應會壓縮系統的量子態並且同時產生量子噪聲與增強熱噪聲。最後,藉由本理論,我們研究了當空腔一開始處在任意高斯態下的演化過程,並且討論了一個簡單的例子即空腔一開始處在相干態。
英文摘要 In this thesis, the exact non-Markovian dynamics of a cavity coupled to a general reservoir with both photon emission/absorption and two-photon processes is solved by combining the Heisenberg's equation of motion approach with the master equation approach. We find that the system-reservoir two-photon coupling induce two-photon processes in the cavity which is negligible only in the weak coupling regime. This reservoir-induced two-photon processes will
squeeze the cavity state and produce both quantum and thermal noises. We also study the time evolution of an arbitrary Gaussian state initially prepared in cavity.
論文目次 1 Introduction 4
1.1 Open Quantum Systems and Non-Markovian Dynamics . . . . . . . . . . . . . . 4
1.2 Two-Photon Processes and Squeezed State of Light . . . . . . . . . . . . . . . . . 5
1.3 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 Exact Non-Markovian Dynamics 7
2.1 Heisenberg's Equation of Motion Approach . . . . . . . . . . . . . . . . . . . . . 7
2.2 Master Equation Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.1 Initial Equilibrium Reservoir . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2.2 Initial State with Two-Photon Correlations . . . . . . . . . . . . . . . . . 14
2.2.3 Quantum Brownian Motion . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3 Non-Markovian E®ects of Two-Photon Processes 17
3.1 Solutions of the Propagating Functions . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Reservoir-Induced Two-Photon Processes . . . . . . . . . . . . . . . . . . . . . . 18
3.3 The Dissipation Dynamics of the Cavity System . . . . . . . . . . . . . . . . . . 20
3.4 Two Di®erent Noise E®ects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5 The Non-Markovian dynamics of Cavity System . . . . . . . . . . . . . . . . . . 24
4 The Time Evolution of Cavity States 28
4.1 Some Formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2 An Example : Cavity Initially in a Coherent State . . . . . . . . . . . . . . . . . 30
5 Conclusion and Perspective 38
A Wigner function 40
B Bibliography 41
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