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研究生: 吳宥昌
Wu, Yu Chang
論文名稱: 弱值放大與不確定性原理之間關聯的研究
A Study of Relation Between Weak-Value Amplification and Uncertainty Principle
指導教授: 陳泳帆
Chen, Yong-Fan
學位類別: 碩士
Master
系所名稱: 理學院 - 物理學系
Department of Physics
論文出版年: 2018
畢業學年度: 106
語文別: 中文
論文頁數: 41
中文關鍵詞: 弱測量弱值放大光學科爾效應不確定性原理
外文關鍵詞: weak measurement, weak-value amplification, optical Kerr effect, uncertainty principle
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  • 本文采用基於光學柯爾效應的弱測量系統來研究弱值放大現象,並從理論上確認此現象與不確定性原理之間的關係。 另外,我們根據弱值放大的失效定義了一個建立弱測量的臨界條件。 最後,我們提供一個物理圖像來說明弱值放大和不定性原理的關係。

    In this thesis, we use the weak measurement system based on the optical Kerr effect to study the weak value amplification (WWA) phenomenon, which theoretically confirms the relationship between WWA and the uncertainty principle. In addition, we determine the critical conditions for establishing weak measurements based on the failure of WWA. Finally, we provide a physical picture to illustrate the relationship between WWA and the uncertainty principle.

    摘要 i 誌謝 vii 目錄 viii 表目錄 x 圖目錄 x 第1章 緒論 1 1.1 簡介 1 1.2不確定性原理 1 1.2.1廣義的不確定性原理推導 2 1.2.2相干態的數量相位不確定性 2 1.3量子糾纏 3 1.4弱值放大 4 1.5研究動機 6 第2章 光學中弱值放大系統 7 2.1 系統架構 7 2.2 待測系統、後選擇系統與零差檢測系統 8 2.2.1待測系統與相位平移 8 2.2.2後選擇系統與零差檢測系統的探測光 9 2.3 平均相位偏移 10 2.3.1 算符及符號表示 11 2.3.2 偵測器算符與零差檢測系統的θ值 11 2.3.3 後選擇下的平均相位量測計算 12 2.4 平均相位ϕ ̅、後選擇機率P與後選擇狀態|├ ψ⟩┤_p的近似 14 2.5 增益係數E_ϕ-|α|^2的峰值半高全寬(full width of half maximum, FWHM)估計 17 第3章 弱值放大與不確定性原理的關係 19 3.1 後選擇機率P、後選擇參數δ,與增益系數E_ϕ 19 3.1.1 後選擇機率的函數結構 19 3.1.2 Re(⟨α│αe^(iϕ_0 ) ⟩)的結構及其意義 20 3.1.3 後選擇下的福克態的機率與相位 22 3.2 相位增益的失效點與相位不確定性的關係 25 3.2.1 探測光的保真度定義方式與F_r 25 3.2.2 F_r、F_rw、F_rp與不確定性原理 27 3.3 弱值放大成立與不確定性原理之間關係的物理模型 31 3.3.1 機率分布重置模型 31 3.3.2 高斯波包模型 32 第4章 結論與未來展望 35 4.1 結論 35 4.2 未來展望 35 參考文獻 37 附錄 A 39 附錄 B 40

    [1] J. von Neumann (2018), “ Mathematical Foundations of Quantum Mechanics (New ed.). ISBN 9781400889921.
    [2] P. Busch,“Quantum Reality, Relativistic Causality, and Closing the Epistemic Circle, Springer Netherlands
    [3] A. Feizpour, X. Xingxing,and A.M. Steinberg, “Amplifying Single-Photon Nonlinearity Using Weak Measurements”, Phys. Rev. Lett. 1
    [4] Y. Aharonov and L. Vailman, “ Properties of a quantum system during the time interval between two measurements Phys. Rev A
    [5] S. Lloyd and J.J.E. Slontine, “Quantum feedback with weak measurements”, Phys. Rev. A.
    [6] Y. Aharonov, D.Z. Albert, and L. Vaidman, “How the Results of a Measurement of a Component of a Spin-□(1/2) Particle Can Turn Out to be 100,” Phys. Rev. Lett.
    [7] A.J. Leggett, “Comment on “How the Results of a Measurement of a Component of a Spin-□(1/2) Particle Can Turn Out to be 100”, Phys. Rev. Lett.
    [8] A. Peres, “Quantum Measurements with Postselection”, Phys. Rev. Lett.
    [9] N. Katz, M. Neeley, M. Ansmann, Radoslaw C. Bialczak, M. Hofheinz, Erik Lucero, A. O’Connell, H. Wang, A. N. Cleland, John M. Martinis and Alexander N. Korotkov , “Reversal of the Weak Measurement of a Quantum State in a Superconducting Phase Qubit”,Phys. Rev. Lett.
    [10] D. Das and Arvind, “Estimation of quantum states by weak and projective measurements”, Phys. Rev. A
    [11] D. T. Pegg and S. M. Barnett ,“Phase properties of the quantized single-mode electromagnetic field”, Phys. Rev.A
    [12] P. K. DAS* and ARPITA GHOSH, “Phase Changes In Nonlinear Process In Interaction Fock Space” International Journal of Modern Physics B
    [13] R. Jozsa (1994). “Fidelity for Mixed Quantum States”. Journal of Modern Optics.
    [14] P. Shengshi Pang and Todd A. Burn, “Improving the Precesion of Weak Measurements by Postselection Measurement”, Phys. Rev Lett.
    [15] N. Brunner and C. Simon ,“Measuring Small Longitudinal Phase Shifts: Weak Measurements or Standard Interferometry?”, Phys. Rev Lett.
    [16] P. Carruthers and M. M. Nieto, “Coherent States and the Number-Phase Uncertainty Relation” ,Phys. Rev. Lett.
    [17] A. Stern, Y. Aharonov, Y. Imry, “Phase uncertainty and loss of interference: A general picture”, Phys. Rev A.
    [18] A. Einstein, B. Podolsky, and N. Rosen, “Can Quantum-Mechanical Description of Physical Reality Be consider Complete”, Phys. Rev.
    [19] Schrödinger E; Born, M.,“Discussion of probability relations between separated systems. ” Mathematical Proceedings of the Cambridge Philosophical Society.
    [20] John A. Vaccaro, “Phase operator on Hilbert space”,Phys. Rev. A.
    [21] A. Royer, “Phase states and phase operators for the quantum harmonic osscillator”,Phys. Rev. A.

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