Minimum-Uncertainty States <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mo>|</mo><mi>γ</mi><mi>〉</mi></math></span> and the States <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mo>|</mo><mi>n</mi><mi>〉</mi></mrow><mrow><mi>γ</mi></mrow></msub></mrow></math></span> of the Electromagnetic Field

P. P. Bertrand; K. Moy; E. A. Mishkin

doi:10.1103/PhysRevD.4.1909

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Minimum-Uncertainty States $| γ 〉$ and the States ${| n 〉}_{γ}$ of the Electromagnetic Field

P. P. Bertrand, K. Moy, and E. A. Mishkin

Polytechnic Institute of Brooklyn, Brooklyn, New York 11201

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Phys. Rev. D 4, 1909 – Published 15 September, 1971

DOI: https://doi.org/10.1103/PhysRevD.4.1909

Abstract

Two vector bases suitable for the representations of states of the electromagnetic field are introduced. The minimum-uncertainty states $| γ 〉$ form an overcomplete nonorthogonal set. The ${| n 〉}_{γ}$ states form a complete orthogonal set. The various relations they satisfy are derived via an oscillator frequency transformation. The corresponding similarity transformation of the non-normal operator changes the physical character of its characteristic states. The photon statistics of the states $| γ 〉$ and ${| n 〉}_{γ}$ are shown to display anticorrelation effects.

References (19)

M. M. Miller and E. A. Mishkin, Phys. Rev. 152, 1110 (1966)
K. Moy, M. S. thesis, Polytechnic Institute of Brooklyn, 1967 (unpublished)
P. P. Bertrand, Ph. D. thesis, Polytechnic Institute of Brooklyn, 1969 (unpublished) P. P. Bertrand and E. A. Mishkin, Bull. Am. Phys. Soc. 15, 89 (1970)
D. Stoler, Phys. Rev. D 1, 3217 (1970)
R. J. Glauber, Phys. Rev. Letters 10, 84 (1963) Phys. Rev. 131, 2766 (1963) J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968)
U. M. Titulaer and R. J. Glauber, Phys. Rev. 140, B676 (1965)
R. J. Glauber, International Summer School on Fundamental Problems of Statistical Mechanics, Noordwijk aan Zee, The Netherlands, 1967 (unpublished)
J. R. Klauder, J. Math. Phys. 4, 1055 (1963) ibid.5, 177 (1964)
E. A. Mishkin and S. Billis, Bull. Am. Phys. Soc. 15, 93 (1970)
A. E. Glassgold and D. Holliday, Phys. Rev. 139, A1717 (1965)
R. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969) ibid.177, 1882 (1969)
J. E. Moyal, Proc. Cambridge Phil. Soc. 45, 91 (1949)
R. J. Glauber, Quantum Optics and Electronics, edited by C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1964)
[11]
R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956) Proc. Roy. Soc. (London) A242, 300 (1957) ibid.A243, 291 (1957)
P. P. Bertrand and E. A. Mishkin, Phys. Letters 25A, 204 (1967)
M. M. Miller and E. A. Mishkin, Phys. Letters 24A, 188 (1967)
F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965)
R. J. Glauber, Phys. Letters 21, 650 (1966)

[c1] M. M. Miller and E. A. Mishkin, Phys. Rev. 152, 1110 (1966)

[c2] K. Moy, M. S. thesis, Polytechnic Institute of Brooklyn, 1967 (unpublished)

[c3] P. P. Bertrand, Ph. D. thesis, Polytechnic Institute of Brooklyn, 1969 (unpublished) P. P. Bertrand and E. A. Mishkin, Bull. Am. Phys. Soc. 15, 89 (1970)

[c4] D. Stoler, Phys. Rev. D 1, 3217 (1970)

[c5] R. J. Glauber, Phys. Rev. Letters 10, 84 (1963) Phys. Rev. 131, 2766 (1963) J. R. Klauder and E. C. G. Sudarshan, Fundamentals of Quantum Optics (Benjamin, New York, 1968)

[c6] U. M. Titulaer and R. J. Glauber, Phys. Rev. 140, B676 (1965)

[c7] R. J. Glauber, International Summer School on Fundamental Problems of Statistical Mechanics, Noordwijk aan Zee, The Netherlands, 1967 (unpublished)

[c8] J. R. Klauder, J. Math. Phys. 4, 1055 (1963) ibid.5, 177 (1964)

[c9] E. A. Mishkin and S. Billis, Bull. Am. Phys. Soc. 15, 93 (1970)

[c10] A. E. Glassgold and D. Holliday, Phys. Rev. 139, A1717 (1965)

[c11] R. E. Cahill and R. J. Glauber, Phys. Rev. 177, 1857 (1969) ibid.177, 1882 (1969)

[c12] J. E. Moyal, Proc. Cambridge Phil. Soc. 45, 91 (1949)

[c13] R. J. Glauber, Quantum Optics and Electronics, edited by C. de Witt, A. Blandin, and C. Cohen-Tannoudji (Gordon and Breach, New York, 1964)

[c14] [11]

[c15] R. Hanbury Brown and R. Q. Twiss, Nature 177, 27 (1956) Proc. Roy. Soc. (London) A242, 300 (1957) ibid.A243, 291 (1957)

[c16] P. P. Bertrand and E. A. Mishkin, Phys. Letters 25A, 204 (1967)

[c17] M. M. Miller and E. A. Mishkin, Phys. Letters 24A, 188 (1967)

[c18] F. T. Arecchi, Phys. Rev. Letters 15, 912 (1965)

[c19] R. J. Glauber, Phys. Letters 21, 650 (1966)

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Minimum-Uncertainty States $| γ 〉$ and the States ${| n 〉}_{γ}$ of the Electromagnetic Field

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Minimum-Uncertainty States |γ〉 and the States |n〉γ of the Electromagnetic Field

Abstract

References (19)

Minimum-Uncertainty States $| γ 〉$ and the States ${| n 〉}_{γ}$ of the Electromagnetic Field