Skip to main content
SpringerLink
Log in

Quantum Phase

  • Conference paper
Book cover Coherence and Quantum Optics VII

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J. Weber, Abstract for the first Rochester meeting on Coherence Properties of Electromagnetic Radiation, June 27–29, 1960.

    Google Scholar 

  2. D. T. Pegg, see this volume.

    Google Scholar 

  3. K. Wódkiewicz, see this volume.

    Google Scholar 

  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. R. Lynch, Phys. Reports 256: 370 (1995).

    MathSciNet  Google Scholar 

  6. J. H. Shapiro, S. R. Shepard, and N. C. Wong, Phys. Rev. Lett. 62: 2377 (1989);

    Article  Google Scholar 

  7. G. S. Summy and D. T. Pegg, Opt. Commun. 77: 75 (1990);

    Article  Google Scholar 

  8. A. Bandilla, H. Paul, and H.-H. Ritze, Quant. Opt. 3: 267 (1991);

    Article  MathSciNet  Google Scholar 

  9. W. P. Schleich, J. P. Dowling, and R. J. Horowicz, Phys. Rev. A 44: 3365 (1991);

    Article  Google Scholar 

  10. S. L. Braunstein, A. S. Lane, and C. M. Caves, Phys. Rev. Lett. 69: 2153 (1992);

    Article  Google Scholar 

  11. S. L. Braunstein, Phys. Rev. Lett. 69: 3598 (1992);

    Article  MathSciNet  Google Scholar 

  12. A. S. Lane, S. L. Braunstein, and C. M. Caves, Phys. Rev. A 47: 1667 (1993);

    Article  Google Scholar 

  13. I. Bialynicki-Birula, M. Freyberger, and W. P. Schleich, Phys. Scr. T48: 113 (1993);

    Article  Google Scholar 

  14. B. Däubler, C. Miller, H. Risken, and L. Schoendoerff, Phys. Scr. T48: 119 (1993);

    Article  Google Scholar 

  15. M. Holland and K. Burnett, Phys. Rev. Lett 71: 1355 (1993).

    Article  Google Scholar 

  16. M. J. Collett, Phys. Scr. T48: 124 (1993);

    Article  Google 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).

    Article  Google Scholar 

  19. J. H. Shapiro and S. R. Shepard, Phys. Rev. A 43: 3795 (1991);

    Article  MathSciNet  Google Scholar 

  20. P. Busch, M. Grabowski, and P. J. Lahti, Phys. Rev. A 50: 2881 (1994);

    Article  Google Scholar 

  21. P. Busch, M. Grabowski, and P. J. Lahti, Ann. Phys. (N.Y.) 237: 1 (1995).

    Article  MathSciNet  Google Scholar 

  22. M. Born. Vorlesungen über Atommechanik, Springer, Berlin (1925).

    Book  MATH  Google Scholar 

  23. W. Pauli. Quantentheorie, Handbuch der Physik, Bd. XXIII, Springer, Berlin (1926).

    Google Scholar 

  24. W. Heisenberg, Z. Phys. 43: 172 (1927).

    Article  MATH  Google Scholar 

  25. E. Schrödinger, Ann. Phys. (Leipzig) 79: 734 (1926).

    Article  MATH  Google Scholar 

  26. J. von Neumann. Mathematische Grundlagen der Quantenmechanik, Springer, Berlin (1932).

    MATH  Google Scholar 

  27. F. London, Z. Phys. 37:915 (1926); Z. Phys. 40: 193 (1927).

    Google Scholar 

  28. P. A. M. Dirac, Proc. Roy. Soc. London Ser. A 114: 243 (1927).

    Article  MATH  Google Scholar 

  29. W. H. Louisell, Phys. Lett. 7: 60 (1963).

    Article  MathSciNet  Google Scholar 

  30. L. Susskind and J. Glogower, Physics 1: 49 (1964).

    Google Scholar 

  31. I. Bialynicki-Birula and Z. Bialynicki-Birula, Phys. Rev. A 14: 1101 (1976).

    Article  Google Scholar 

  32. I. Bialynicki-Birula. Foundations of Radiation Theory and Quantum Electrodynamics (Ed. A. O. Barut ), Plenum, New York (1980).

    Google Scholar 

  33. P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40: 411 (1968).

    Article  Google Scholar 

  34. 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. K. Vogel, V. M. Akulin, and W. P. Schleich, Phys. Rev. Lett. 71: 1816 (1993);

    Article  Google Scholar 

  36. A. S. Parkins, P. Marte, P. Zoller, and H. J. Kimble, Phys. Rev. Lett. 71: 3095 (1993).

    Article  Google Scholar 

  37. J.-M. Lévy-Leblond, Ann. Phys. (NY) 101: 319 (1976).

    Article  MATH  Google Scholar 

  38. J. C. Garrison and J. Wong, J. Math. Phys. 11: 2243 (1970).

    Google Scholar 

  39. D. T. Pegg and S. M. Barnett, Europhys. Lett. 6: 483 (1988);

    Article  Google Scholar 

  40. D. T. Pegg and S. M. Barnett, Phys. Rev. A 39: 1665 (1989).

    Article  Google Scholar 

  41. S. M. Barnett and B. J. Dalton, Phys. Scr. T48: 13 (1993).

    Article  Google Scholar 

  42. A. Luks and V. Pefinovâ,, Quantum Opt. 5: 287 (1993).

    Article  Google Scholar 

  43. M. B. Cicils, Y. Cuche, V. Marvulle, and W. F. Wreszinski, Phys. Rev. A 43: 4044 (1991).

    Article  Google Scholar 

  44. J. Bergou and B. G. Englert, Ann. Phys. (NY) 209: 479 (1991).

    Article  MathSciNet  MATH  Google Scholar 

  45. T. B. Smith, D. A. Dubin, and M. A. Hennings, J. mod. Opt. 39: 1603 (1992);

    Article  Google Scholar 

  46. D. A. Dubin, M. A. Hennings, and T. B. Smith, Publ. RIMS, Kyoto Univ. 30: 479 (1994);

    Article  MathSciNet  MATH  Google Scholar 

  47. D. A. Dubin, M. A. Hennings, and T. B. Smith, Mathematical Aspects of Quantum Phase (preprint) (1995).

    Google Scholar 

  48. M. Ban, Phys. Lett. A 176:47 (1993); Phys. Rev. A 48: 3452 (1993).

    Google Scholar 

  49. A. Luis and L. L. Sä,nchez-Soto, Phys. Rev. A 48: 4702 (1993).

    Article  Google Scholar 

  50. A. Luks and V. Petinovâ, Phys. Scr. T 48: 94 (1993).

    Article  Google Scholar 

  51. C. Brif and Y. Ben-Aryeh, Phys. Rev. A 50: 2727 (1994).

    Article  Google Scholar 

  52. 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);

    Article  Google 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. J. P. Dowling, W. P. Schleich, and J. A. Wheeler, Ann. Phys. (Leipzig) 48: 423 (1991).

    Article  Google Scholar 

  56. P. L. Knight and B. M. Garraway, Phys. Rev. A 46: 5346 (1992).

    Article  Google Scholar 

  57. M. llillery, M. Freyberger, and W. P. Schleich, Phys. Rev. A 51: 1792 (1995).

    Article  Google Scholar 

  58. H. Paul, Fortschr. Phys. 22: 657 (1974).

    Article  Google Scholar 

  59. A. Bandilla and H. Paul, Ann. Phys. (Leipzig) 23: 323 (1969).

    Article  Google Scholar 

  60. W. P. Schleich, A. Bandilla, and H. Paul, Phys. Rev. A 45: 6652 (1992).

    Article  Google Scholar 

  61. W. Vogel and W. P. Schleich, Phys. Rev. A 44: 7642 (1991).

    Article  Google Scholar 

  62. M. G. Raymer, D. T. Smithey, M. Beck, and J. Cooper, Acta Physica Polonica A 86: 71 (1994).

    Google Scholar 

  63. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 67: 1426 (1991);

    Article  Google Scholar 

  64. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 45: 424 (1992);

    Article  Google Scholar 

  65. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 46: 2840 (1992);

    Article  MathSciNet  Google Scholar 

  66. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 47: 4535 (1993);

    Article  Google Scholar 

  67. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 47: 4541 (1993);

    Article  Google Scholar 

  68. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A 48: 1719 (1993);

    Article  Google Scholar 

  69. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 71: 2579 (1993);

    Article  Google Scholar 

  70. J. W. Noh, A. Fougères, and L. Mandel, Phys. Scr. T48: 29 (1993);

    Article  Google Scholar 

  71. J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. A. 49: 530 (1993).

    Google Scholar 

  72. 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. S. M. Barnett and D. T. Pegg, Phys. Rev. A 47: 4537 (1993);

    Article  Google Scholar 

  74. Z. Hradil and J. Bajer, Phys. Rev. A 48: 1717 (1993);

    Article  Google Scholar 

  75. Z. Hradil, Phys. Rev. A 47: 4532 (1993);

    Article  Google Scholar 

  76. A. Bandilla, Phys. Scr. T48: 49 (1993);

    Article  Google Scholar 

  77. J. D. Franson, Phys. Rev. A 49: 3221 (1994).

    Article  Google Scholar 

  78. P. Riegler and K. Wódkiewicz, Phys. Rev. A 49: 1387 (1994).

    Article  Google Scholar 

  79. A. Bandilla, Phys. Scr. T48: 49 (1993).

    Article  Google Scholar 

  80. M. Freyberger and W. P. Schleich, Phys. Rev. A 47: R30 (1993);

    Article  Google Scholar 

  81. M. Freyberger, K. Vogel, and W. P. Schleich, Phys. Lett. A 176: 41 (1993);

    Article  Google Scholar 

  82. M. Freyberger, K. Vogel, and W. P. Schleich, Quantum Opt. 5: 65 (1993).

    Article  Google Scholar 

  83. U. Leonhardt and H. Paul, Phys. Rev. A 47:R. 2460 (1993).

    Google Scholar 

  84. M. Freyberger, M. Heni, and W. P. Schleich, Quantum Semiclass. Opt. 7: 187 (1995).

    Article  Google Scholar 

  85. N. G. Walker and J. E. Carol, Electron. Lett 20: 981 (1984);

    Article  Google Scholar 

  86. N. G. Walker and J. E. Carol, Opt. Quant. Electron. 18: 355 (1986).

    Article  Google Scholar 

  87. E. Arthurs and J. Kelly, Bell System Technical J. 44: 725 (1965);

    Article  Google Scholar 

  88. C. Y. She and H. Heffner, Phys. Rev. 152: 1103 (1966);

    Article  MATH  Google Scholar 

  89. H. P. Yuen, Phys. Lett. A 91: 101 (1982);

    Article  MathSciNet  Google Scholar 

  90. S. Stenholm, Ann. Phys. (NY) 218: 233 (1992);

    Article  MathSciNet  MATH  Google Scholar 

  91. U. Leonhardt and H. Paul, Phys. Rev. A 48: 4598 (1993);

    Article  Google Scholar 

  92. U. Leonhardt and H. Paul, J. Mod. Opt. 40: 1745 (1993);

    Article  Google Scholar 

  93. U. Leonhardt and H. Paul, Phys. Rev. A 51: 84 (1995);

    Article  Google Scholar 

  94. H. Paul, Phys. Bl. 49: 1105 (1993).

    Article  Google Scholar 

  95. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47: 777 (1935).

    Article  MATH  Google Scholar 

  96. N. Bohr, Phys. Rev. 48: 696 (1935).

    Article  MATH  Google Scholar 

  97. Y. Aharonov, D. Z. Albert, and C. K. Au, Phys. Rev. Lett. 47: 1029 (1981).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Abteilung für Quantenphysik, Universität Ulm, 89069, Ulm, Germany

    M. Heni, M. Freyberger & W. P. Schleich

  2. Max-Planck Institut für Quantenoptik, 85740, Garching, Germany

    W. P. Schleich

Authors
  1. M. Heni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Freyberger
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. W. P. Schleich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Rochester, Rochester, New York, USA

    Joseph H. Eberly , Leonard Mandel  & Emil Wolf ,  & 

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media New York

About this paper

Cite this paper

Heni, M., Freyberger, M., Schleich, W.P. (1996). Quantum Phase. In: Eberly, J.H., Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics VII. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-9742-8_29

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-9742-8_29

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-9744-2

  • Online ISBN: 978-1-4757-9742-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation