Quantum Phase

  • M. Heni
  • M. Freyberger
  • W. P. Schleich
Conference paper

Abstract

In June 1960 the first in this series of most successful Rochester conferences on Coherence and Quantum Optics took place. At this meeting devoted to Coherence Properties of Electromagnetic Radiation Joe Weber presented a paper1 with the title “Phase as a Dynamical Variable”. It is remarkable that 35 years later this question it is still such a hot topic that it is the subject of various invited and contributed papers2,3 at the seventh conference of this series. Indeed over the last years the question of a proper quantum mechanical description of phase has attracted a lot of attention. This is on one hand due to the experimental progress in creating non classical states of light which display phase properties different from those of a coherent state, and on the other hand was triggered by the Pegg-Barnett proposal for a hermitian phase operator. Moreover the recent operational approach by Noh, Fougères, and Mandel (NFM) opened a new era in this long standing debate. There are many indications that phase will still be a major topic at the next meeting in the new millennium for which Emil Wolf had us sign up already.

Keywords

Coherent State Density Operator Quantum Phase Input Mode Phase Operator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    J. Weber, Abstract for the first Rochester meeting on Coherence Properties of Electromagnetic Radiation, June 27–29, 1960.Google Scholar
  2. 2.
    D. T. Pegg, see this volume.Google Scholar
  3. 3.
    K. Wódkiewicz, see this volume.Google Scholar
  4. 4.
    Special issue on Quantum Phase and Phase Dependent Measurements (edited by W. P. Schleich and S. M. Barnett), Phys. Scr. T48 (1993).Google Scholar
  5. 5.
    R. Lynch, Phys. Reports 256: 370 (1995).MathSciNetGoogle Scholar
  6. 6.
    J. H. Shapiro, S. R. Shepard, and N. C. Wong, Phys. Rev. Lett. 62: 2377 (1989);CrossRefGoogle Scholar
  7. G. S. Summy and D. T. Pegg, Opt. Commun. 77: 75 (1990);CrossRefGoogle Scholar
  8. A. Bandilla, H. Paul, and H.-H. Ritze, Quant. Opt. 3: 267 (1991);MathSciNetCrossRefGoogle Scholar
  9. W. P. Schleich, J. P. Dowling, and R. J. Horowicz, Phys. Rev. A 44: 3365 (1991);CrossRefGoogle Scholar
  10. S. L. Braunstein, A. S. Lane, and C. M. Caves, Phys. Rev. Lett. 69: 2153 (1992);CrossRefGoogle Scholar
  11. S. L. Braunstein, Phys. Rev. Lett. 69: 3598 (1992);MathSciNetCrossRefGoogle Scholar
  12. A. S. Lane, S. L. Braunstein, and C. M. Caves, Phys. Rev. A 47: 1667 (1993);CrossRefGoogle Scholar
  13. I. Bialynicki-Birula, M. Freyberger, and W. P. Schleich, Phys. Scr. T48: 113 (1993);CrossRefGoogle Scholar
  14. B. Däubler, C. Miller, H. Risken, and L. Schoendoerff, Phys. Scr. T48: 119 (1993);CrossRefGoogle Scholar
  15. M. Holland and K. Burnett, Phys. Rev. Lett 71: 1355 (1993).CrossRefGoogle Scholar
  16. 7.
    M. J. Collett, Phys. Scr. T48: 124 (1993);CrossRefGoogle Scholar
  17. A. Bandilla and H.-H. Ritze, Phys. Rev. A 49: 4447 (1994);Google Scholar
  18. M. Freyberger and W. P. Schleich Phys. Rev. A 49: 5056 (1994).CrossRefGoogle Scholar
  19. 8.
    J. H. Shapiro and S. R. Shepard, Phys. Rev. A 43: 3795 (1991);MathSciNetCrossRefGoogle Scholar
  20. P. Busch, M. Grabowski, and P. J. Lahti, Phys. Rev. A 50: 2881 (1994);CrossRefGoogle Scholar
  21. P. Busch, M. Grabowski, and P. J. Lahti, Ann. Phys. (N.Y.) 237: 1 (1995).MathSciNetCrossRefGoogle Scholar
  22. 9.
    M. Born. Vorlesungen über Atommechanik, Springer, Berlin (1925).CrossRefMATHGoogle Scholar
  23. W. Pauli. Quantentheorie, Handbuch der Physik, Bd. XXIII, Springer, Berlin (1926).Google Scholar
  24. 10.
    W. Heisenberg, Z. Phys. 43: 172 (1927).CrossRefMATHGoogle Scholar
  25. 11.
    E. Schrödinger, Ann. Phys. (Leipzig) 79: 734 (1926).CrossRefMATHGoogle Scholar
  26. 12.
    J. von Neumann. Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).MATHGoogle Scholar
  27. 13.
    F. London, Z. Phys. 37:915 (1926); Z. Phys. 40: 193 (1927).Google Scholar
  28. 14.
    P. A. M. Dirac, Proc. Roy. Soc. London Ser. A 114: 243 (1927).CrossRefMATHGoogle Scholar
  29. 15.
    W. H. Louisell, Phys. Lett. 7: 60 (1963).MathSciNetCrossRefGoogle Scholar
  30. 16.
    L. Susskind and J. Glogower, Physics 1: 49 (1964).Google Scholar
  31. 17.
    I. Bialynicki-Birula and Z. Bialynicki-Birula, Phys. Rev. A 14: 1101 (1976).CrossRefGoogle Scholar
  32. I. Bialynicki-Birula. Foundations of Radiation Theory and Quantum Electrodynamics (Ed. A. O. Barut ), Plenum, New York (1980).Google Scholar
  33. 18.
    P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40: 411 (1968).CrossRefGoogle Scholar
  34. 19.
    See the special issues J. Opt. Soc. Am. B4:10 (1987); J. Mod. Opt. 34:6 (1987); Appl. Phys. B 55:3 (1992).Google Scholar
  35. 20.
    K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71: 1816 (1993);CrossRefGoogle Scholar
  36. A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Phys. Rev. Lett. 71: 3095 (1993).CrossRefGoogle Scholar
  37. 21.
    J.-M. Lévy-Leblond, Ann. Phys. (NY) 101: 319 (1976).CrossRefMATHGoogle Scholar
  38. 22.
    J. C. Garrison and J. Wong, J. Math. Phys. 11: 2243 (1970).Google Scholar
  39. 23.
    D. T. Pegg and S. M. Barnett, Europhys. Lett. 6: 483 (1988);CrossRefGoogle Scholar
  40. D. T. Pegg and S. M. Barnett, Phys. Rev. A 39: 1665 (1989).CrossRefGoogle Scholar
  41. 24.
    S. M. Barnett and B. J. Dalton, Phys. Scr. T48: 13 (1993).CrossRefGoogle Scholar
  42. 25.
    A. Luks and V. Pefinovâ,, Quantum Opt. 5: 287 (1993).CrossRefGoogle Scholar
  43. 26.
    M. B. Cicils, Y. Cuche, V. Marvulle, and W. F. Wreszinski, Phys. Rev. A 43: 4044 (1991).CrossRefGoogle Scholar
  44. 27.
    J. Bergou and B. G. Englert, Ann. Phys. (NY) 209: 479 (1991).MathSciNetCrossRefMATHGoogle Scholar
  45. 28.
    T. B. Smith, D. A. Dubin, and M. A. Hennings, J. mod. Opt. 39: 1603 (1992);CrossRefGoogle Scholar
  46. D. A. Dubin, M. A. Hennings, and T. B. Smith, Publ. RIMS, Kyoto Univ. 30: 479 (1994);MathSciNetCrossRefMATHGoogle Scholar
  47. D. A. Dubin, M. A. Hennings, and T. B. Smith, Mathematical Aspects of Quantum Phase (preprint) (1995).Google Scholar
  48. 29.
    M. Ban, Phys. Lett. A 176:47 (1993); Phys. Rev. A 48: 3452 (1993).Google Scholar
  49. 30.
    A. Luis and L. L. Sä,nchez-Soto, Phys. Rev. A 48: 4702 (1993).CrossRefGoogle Scholar
  50. 31.
    A. Luks and V. Petinovâ, Phys. Scr. T 48: 94 (1993).CrossRefGoogle Scholar
  51. 32.
    C. Brif and Y. Ben-Aryeh, Phys. Rev. A 50: 2727 (1994).CrossRefGoogle Scholar
  52. 33.
    W. P. Schleich, R. J. Horowitz, and S. Varro. Quantum Optics V (Ed. D. F. Walls and J. Harvey ), Springer, Heidelberg (1989);Google Scholar
  53. W. P. Schleich, R. J. Horowitz, and S. Varro. Phys. Rev. A 40: 7405 (1989);CrossRefGoogle Scholar
  54. W. P. Schleich, J. P. Dowling, R. J. Horowitz, and S. Varro. New Frontiers in Quantum Electrodynamics (edited by A. O. Barut ), Plenum Press, New York (1990).Google Scholar
  55. 34.
    J. P. Dowling, W. P. Schleich, and J. A. Wheeler, Ann. Phys. (Leipzig) 48: 423 (1991).CrossRefGoogle Scholar
  56. 35.
    P. L. Knight and B. M. Garraway, Phys. Rev. A 46: 5346 (1992).CrossRefGoogle Scholar
  57. 36.
    M. llillery, M. Freyberger, and W. P. Schleich, Phys. Rev. A 51: 1792 (1995).CrossRefGoogle Scholar
  58. 37.
    H. Paul, Fortschr. Phys. 22: 657 (1974).CrossRefGoogle Scholar
  59. 38.
    A. Bandilla and H. Paul, Ann. Phys. (Leipzig) 23: 323 (1969).CrossRefGoogle Scholar
  60. 39.
    W. P. Schleich, A. Bandilla, and H. Paul, Phys. Rev. A 45: 6652 (1992).CrossRefGoogle Scholar
  61. 40.
    W. Vogel and W. P. Schleich, Phys. Rev. A 44: 7642 (1991).CrossRefGoogle Scholar
  62. 41.
    M. G. Raymer, D. T. Smithey, M. Beck, and J. Cooper, Acta Physica Polonica A 86: 71 (1994).Google Scholar
  63. 42.
    J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 67: 1426 (1991);CrossRefGoogle Scholar
  64. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 45: 424 (1992);CrossRefGoogle Scholar
  65. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 46: 2840 (1992);MathSciNetCrossRefGoogle Scholar
  66. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 47: 4535 (1993);CrossRefGoogle Scholar
  67. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 47: 4541 (1993);CrossRefGoogle Scholar
  68. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 48: 1719 (1993);CrossRefGoogle Scholar
  69. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 71: 2579 (1993);CrossRefGoogle Scholar
  70. J. W. Noh, A. Fougères, and L. Mandel, Phys. Scr. T48: 29 (1993);CrossRefGoogle Scholar
  71. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A. 49: 530 (1993).Google Scholar
  72. 43.
    L. Mandel. Foundations of quantum mechanics (edited by T. D. Black, M. M. Nieto, H. S. Pilloff, M. O. Scully, and R. M. Sinclair ), World Scientific, Singapore (1992).Google Scholar
  73. 44.
    S. M. Barnett and D. T. Pegg, Phys. Rev. A 47: 4537 (1993);CrossRefGoogle Scholar
  74. Z. Hradil and J. Bajer, Phys. Rev. A 48: 1717 (1993);CrossRefGoogle Scholar
  75. Z. Hradil, Phys. Rev. A 47: 4532 (1993);CrossRefGoogle Scholar
  76. A. Bandilla, Phys. Scr. T48: 49 (1993);CrossRefGoogle Scholar
  77. J. D. Franson, Phys. Rev. A 49: 3221 (1994).CrossRefGoogle Scholar
  78. 45.
    P. Riegler and K. Wódkiewicz, Phys. Rev. A 49: 1387 (1994).CrossRefGoogle Scholar
  79. 46.
    A. Bandilla, Phys. Scr. T48: 49 (1993).CrossRefGoogle Scholar
  80. 47.
    M. Freyberger and W. P. Schleich, Phys. Rev. A 47: R30 (1993);CrossRefGoogle Scholar
  81. M. Freyberger, K. Vogel, and W. P. Schleich, Phys. Lett. A 176: 41 (1993);CrossRefGoogle Scholar
  82. M. Freyberger, K. Vogel, and W. P. Schleich, Quantum Opt. 5: 65 (1993).CrossRefGoogle Scholar
  83. 48.
    U. Leonhardt and H. Paul, Phys. Rev. A 47:R. 2460 (1993).Google Scholar
  84. 49.
    M. Freyberger, M. Heni, and W. P. Schleich, Quantum Semiclass. Opt. 7: 187 (1995).CrossRefGoogle Scholar
  85. 50.
    N. G. Walker and J. E. Carol, Electron. Lett 20: 981 (1984);CrossRefGoogle Scholar
  86. N. G. Walker and J. E. Carol, Opt. Quant. Electron. 18: 355 (1986).CrossRefGoogle Scholar
  87. 51.
    E. Arthurs and J. Kelly, Bell System Technical J. 44: 725 (1965);CrossRefGoogle Scholar
  88. C. Y. She and H. Heffner, Phys. Rev. 152: 1103 (1966);CrossRefMATHGoogle Scholar
  89. H. P. Yuen, Phys. Lett. A 91: 101 (1982);MathSciNetCrossRefGoogle Scholar
  90. S. Stenholm, Ann. Phys. (NY) 218: 233 (1992);MathSciNetCrossRefMATHGoogle Scholar
  91. U. Leonhardt and H. Paul, Phys. Rev. A 48: 4598 (1993);CrossRefGoogle Scholar
  92. U. Leonhardt and H. Paul, J. Mod. Opt. 40: 1745 (1993);CrossRefGoogle Scholar
  93. U. Leonhardt and H. Paul, Phys. Rev. A 51: 84 (1995);CrossRefGoogle Scholar
  94. H. Paul, Phys. Bl. 49: 1105 (1993).CrossRefGoogle Scholar
  95. 52.
    A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47: 777 (1935).CrossRefMATHGoogle Scholar
  96. 53.
    N. Bohr, Phys. Rev. 48: 696 (1935).CrossRefMATHGoogle Scholar
  97. 54.
    Y. Aharonov, D. Z. Albert, and C. K. Au, Phys. Rev. Lett. 47: 1029 (1981).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • M. Heni
    • 1
  • M. Freyberger
    • 1
  • W. P. Schleich
    • 1
    • 2
  1. 1.Abteilung für QuantenphysikUniversität UlmUlmGermany
  2. 2.Max-Planck Institut für QuantenoptikGarchingGermany

Personalised recommendations