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研究生： 阮周芳詩
Chau, Phuong Thi Nguyen
論文名稱： 量子光學中的相位算符
Phase Operator Revisited in Quantum Optics
指導教授： 陳家駒
Chen, Chia-Chu
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： 2013
畢業學年度： 101
語文別： 英文
論文頁數： 0
外文關鍵詞： Phase Operator, Quantum Optics, continuous eigenvalues
相關次數： 點閱：91  下載：3 
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    • The phase operator defined by quantization electromagnetic fi eld is still incompletely. This phase operator Phi is in doubt because annihilation and creation operators of a harmonic oscillator a and a^{dagger} respectively have the same index and e^{iPhi} is not Unitary by de finition of Dirac. Susskind and Glogower [2] operator E not only satisfi ed the index relation of a and a^{dagger} but also is a well-known defi nition even E is still not Unitary. In this thesis, we will point out the inconsistency in Susskind and Glogower defi nition and discuss the proper phase operator defi ned by Smith and Vaccaro.

    Abstract . . . . . . . . . . . . . . . . . . . . . . . i List of fi gures . . . . . . . . . . . . . . . . . . . . iv Acknowledgments . . . . . . . . . . . . . . . . . . . . v Introduction . . . . . . . . .. . . . . . . . . . . . . 1 1 Overview of Quantum Phase Operator . . . . . . . . . 7 1.1 Dirac's Phase Operator . . . . . . . . .. . . . . . 8 1.2 SG's Phase Operator . . . . . . . . . ... . . . . . 9 1.3 Pegg and Barnett's Phase Operator . . . . ..... . . 13 1.4 Phase Measurement . . . . . . . . . . . . . ... . . 15 1.4.1 Young's Double-splits Experiment . ............ . 15 1.4.2 Experimental Scheme . . . . . . . ........... . . 17 2 A Critical Analysis of SG Operator .. . . . . . . . . 22 2.1 More Discussions on The SG Operator . ....... . . . 22 2.2 Another Form of Eigenvalues of E . . . . .... . . . 24 2.3 The Domain of The Phase  . . . . . . . . . ...... . 27 2.3.1 Classical Simple Harmonic Oscillator . ...........27 2.3.2 Quantum Phase . . . . . . . . . . . . . ..........28 3 Discussion A New Quantum Phase . . . . . . . . . . . 32 3.1 A New Quantum Phase . . . . . . . . . . . ....... . 32 3.1.1 Lewis, Lawrence and Harris's De nition ............32 3.1.2 Smith and Vaccaro's Comment . . . ............... 34 3.1.3 Davidovic Family and Arsenovic Com-ment . . . . . 35 3.2 Discussion on Eigenvalues of The Phase Operators... 37 3.2.1 SG's Operator . . . . . . . . . . . . . . ........37 3.2.2 SV's Phase Operator . . . . . . . . . . ..........38 3.2.3 Consistency Checking . . . . . . . . . ...........44 Conclusion . . . . . . . . . . . . . . . . . . . . . . 50 References . . . . . . . . . . . . . . . . . . . . . . 51

    [1] P. A. M. Dirac, Proc. Roy. Soc. (London) A114, 243 (1927).
    [2] L. Susskind and J. Glogower, Physics 1, 49 (1964).
    [3] J. W. Nor, A. Fougres and L. Mandel, Phys. Rev. A 45, 424 (1992).
    [4] P. A. M. Dirac, Principle of Quantum Mechanics, 3rd ed., Clarendon, Oxford (1947).
    [5] M. M. Nieto, Physica Scripta. T48, 5(1993).
    [6] C. C. Gerry and P. L. Knight, Introductory Quantum Optics, Cambridge Uni-versity Press (2005).
    [7] D. T. Pegg and S. M. Barnett, Phys. Rev. A 39, 1665 (1989).
    [8] H. Ralph Lewis, Walter E. Lawrence, and Joseph D. Harris, Phys. Rev. Lett. 77, 5157 (1996).
    [9] Ljubica Davidovi c, Du san Arsenovi c, Milena Davidovi c and Dragomir M Davidovi c, J. Phys. A, 42, 235302 (2009).
    [10] T. B. Smith and John A. Vaccaro, Phys. Rev. Lett. 80, 2745 (1998).
    [11] H. Ralph Lewis, Walter E. Lawrence, and Joseph D. Harris, Phys. Rev. Lett. 80, 2746 (1998).
    [12] P. D. Powell, Calculating Determinants of Block Matrices, arXiv:math.RA/1112.4379 (2011).

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