臺灣博碩士論文加值系統

一般來說，金屬表面因具有無窮多自由電荷振盪模式，所以其與微小量子系統耦合時，將導致量子系統的能量耗散。但最近的研究揭示，當二能階系統非常靠近金屬表面時，它們之間非常強的交互作用將使金屬表面電漿子場的譜密度從平直線轉為具有結構，此對量子系統將有單純耗散之外的影響。在本論文中，我們便研究兩個二能階系統靠近一個奈米金屬球時，奈米金屬球表面電漿子場環境對二能階系統的演化及雙二能階系統糾纏的影響。我們使用Master Equation來計算整個系統的密度矩陣，並進而計算其糾纏態的演化。我們發現在特定條件下，無論系統初始態是在單一的二能階系統，或是在雙二能階糾纏態，其量子糾纏可因為機率干涉而提高，證明了在金屬表面電漿子場譜密度有結構的情況下，金屬這種耗散環境亦可協助保持微小量子系統的相干性。

The metal surface, in general, contains infinite modes of free-charge oscillation, and thus causes dissipations to the quantum system coupled to it. However, recent studies have shown that as a two-level system is positioned very close to the metal surface, the strong coupling between them will change the spectral density of surface-plasma fields from smooth to structured. This can lead to different dynamics of that quantum system from purely exponential decay. In this thesis, we therefore investigate the variations of excitonic dynamics and bipartite entanglement of the double two-level systems which are placed close to the metal surface. We apply the Master equation to compute the density matrix of the system, and then calculate the entanglement dynamics. We find that the entanglement can be revival due to quantum interference for both the initial state being in one of the two-level systems or in entangled state. The results show that the structured surface-plasmon-field environment can not only play a role of pure dissipations but help to protect the quantum coherence of the system coupled to it.

中文摘要 i
ABSTRACT ii
目次 iii
圖目次 v
表目次 ix
1 . 緒論 1
1.1. 文獻探討 1
1.2. 研究動機 3
2 . 二能階系統與理論分析模型 4
2.1. 二能階系統 4
2.1.1. 二能階系統的哈密頓量 4
2.1.2. 位於完美空腔內之二能階系統 5
2.2. 系統與環境的交互作用及Master Equation 7
2.2.1. Master Equation 的推導 7
2.2.2. 非完美空腔與二能階系統的交互作用 10
2.3. 理論分析模型 12
2.3.1. 模型之哈密頓量以及Master equation 13
2.3.2. 金屬球與二能階系統之耦合強度計算 14
2.3.1. 兩個二能階系統之糾纏程度 17
2.3.2. 比較電單極與電多極電漿子對二能階系統之交互作用大小 18
3 . 結果與討論 20
3.1. 兩個二能階系統與金屬球表面距離相同 20
3.1.1. 不同距離下各狀態機率演化比較 20
3.1.2. 相同金屬球半徑，不同距離下雙二能階糾纏態的比較 23
3.1.2.1 初始態在二能階系統 23
3.1.2.2 初始態為最大糾纏 25
3.1.3. 不同奈米金屬球半徑的雙二能階系統糾纏比較 26
3.1.4. 雙二能階糾纏態隨金屬球半徑與距離的改變 28
3.2. 兩個二能階系統與金屬球表面距離不同的情形 29
3.2.1. 初始態為純態 29
3.2.2. 初始態為糾纏態 35
4 . 結論 39
參考文獻 40

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