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系統識別號 U0026-1407201321581100
論文名稱(中文) 量子光學中的相位算符
論文名稱(英文) Phase Operator Revisited in Quantum Optics
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 2
出版年 102
研究生(中文) 阮周芳詩
研究生(英文) Phuong Thi Nguyen Chau
學號 L26007012
學位類別 碩士
語文別 英文
論文頁數 0頁
口試委員 指導教授-陳家駒
口試委員-蔡錦俊
口試委員-包健華
中文關鍵字 none 
英文關鍵字 Phase Operator  Quantum Optics  continuous eigenvalues 
學科別分類
中文摘要 none
英文摘要 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.
論文目次 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
參考文獻 [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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