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