Quasiprobability Distributions in Quantum Optics

  • G. J. Milburn
  • D. F. Walls
Conference paper
Part of the Fundamental Theories of Physics book series (FTPH, volume 24)


We review some generalizations of phase space probability distributions used in quantum optics. We also present an application of a particular distribution, the Q-function, to the concept of interference in phase space and the oscillations in the photon number distribution for a squeezed state. The method enables a straightforward discussion of the effect of dissipation on these oscillations.


Phase Space Coherent State Density Operator Wigner Function Phase Space Point 
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  1. 1.
    R. J. Glauber, Phys. Rev. 131, 2766 (1963).CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    E. C. G. Sudarshan, Phys. Rev. Letts., 10, 277 (1963).CrossRefzbMATHADSMathSciNetGoogle Scholar
  3. 3.
    For a review see, D. F. Walls Nature (London) 306, 141 (1983);CrossRefADSGoogle Scholar
  4. 3.A
    R. Loudon and P.L. Knight, J. Mod. Opt. 34, 709 (1987).CrossRefzbMATHADSMathSciNetGoogle Scholar
  5. 4.
    R. E. Slusher, L.W. Hollbert, B. Yurke, J.C. Mertz and J. F. Valley, Phys. Rev. Letts., 55, 2409 (1985).CrossRefADSGoogle Scholar
  6. 5.
    R. M. Shelby, M. O. Levenson, S. H. Perlmutter, R. G. De Voe and D. F. Walls, Phys. Rev. Letts., 57, 691 (1986).CrossRefADSGoogle Scholar
  7. 6.
    L. Wu, H. J. Kimble, J. L. Hall and H. Wu; Phys. Rev. Letts. 57, 2520 (1986).CrossRefADSGoogle Scholar
  8. 7.
    M.W. Maeda, P. Kumar and J. H. Shapiro; Opt. Lett. 12, 161 (1987).CrossRefADSGoogle Scholar
  9. 8.
    M.D. Reid and D.F. Walls, Phys. Rev. A 34, 4929 (1986).CrossRefADSGoogle Scholar
  10. 9.
    W. Schleich and J. A. Wheeler, Nature (London), 326, 574 (1987).CrossRefADSGoogle Scholar
  11. 10.
    P. D. Drummond and C. W. Gardiner, J. Phys. A 13, 2353 (1980).CrossRefADSMathSciNetGoogle Scholar
  12. 11.
    M. Hillery, R. F. O’Connell, M. O. Scully and E. P. Wigner, Phys. Rep. 106, 121 (1984).CrossRefADSMathSciNetGoogle Scholar
  13. 12.
    C. L. Mehta and E. C. G. Sudarshan, Phys. Rev. 138, B274 (1965).CrossRefADSMathSciNetGoogle Scholar
  14. 13.
    E. B. Davies, ’Quantum Theory of Open Systems’ (Academic, New York, 1976).zbMATHGoogle Scholar
  15. 14.
    E. Arthurs and J. L. Kelly Jr., Bell Syst. Tech. J. 44, 725 (1965).Google Scholar
  16. 15.
    W. Schleich, D. F. Walls and J. A. Wheeler, submitted to Phys. Rev.A.Google Scholar
  17. 16.
    D. F. Walls and G. J. Milburn, Phys. Rev. A 31, 2403 (1985).CrossRefADSMathSciNetGoogle Scholar
  18. 17.
    A. O. Caldeira and A. J. Leggett, Phys. Rev. A 31, 1059 (1985).CrossRefADSGoogle Scholar
  19. 18.
    G. J. Milburn and C. A. Holmes, Phys. Rev. Letts. 56, 2237 (1986).CrossRefADSMathSciNetGoogle Scholar
  20. 19.
    G.J. Milburn and D.F. Walls, submitted to Phys. Rev. A.Google Scholar
  21. 20.
    M. D. Srinivas and E.B. Davies, Optica Acta 28, 981 (1981);CrossRefADSMathSciNetGoogle Scholar
  22. 20.A
    Optica Acta 29, 235 (1982).Google Scholar
  23. 20.B
    See also L. Manuel, Optica Acta 28, 1447 (1981).CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • G. J. Milburn
    • 1
  • D. F. Walls
    • 2
  1. 1.Department of Physics and Theoretical PhysicsAustralian National UniversityCanberraAustralia
  2. 2.Department of PhysicsUniversity of AucklandAucklandNew Zealand

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