Czechoslovak Journal of Physics B

, Volume 18, Issue 2, pp 197–213 | Cite as

Normal and antinormal ordering of field operators in quantum optics

  • J. PeŘina


The relations between the probability distributionpn vt of the number of photonsn vt in a volumeV at timet and the probability distributions PN(W) and PA(W) of the integrated intensityW related to the normal and antinormal ordering of field operators and the relations between corresponding moments are studied for a field containingM modes. As the normally ordered correlations are measured with photodetectors and the antinormally ordered correlations are measured with quantum counters the relations betweenn vt , PN(W) and PA(W) permit the statistical behaviour of light to be determined from measurements with photodetectors and quantum counters. The results obtained here are used for the superposition of coherent and thermal fields. It is also shown that the antinormal correlations depend explicitly on the number of modes and that in the classical limit, when the average photon occupation number per mode becomes large, the distributionsn vt , PN(W) and PA(W) become equal.


Probability Distribution Field Operator Classical Limit Statistical Behaviour Occupation Number 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Mandel L.: Phys. Rev.152 (1966), 438.Google Scholar
  2. [2]
    Mandel L.: Phys. Rev.136 (1964), B1221.Google Scholar
  3. [3]
    Glauber R. J.: Phys. Rev.131 (1963), 2766.Google Scholar
  4. [4]
    Mandel L., Wolf E.: Rev. Mod. Phys.37 (1965), 231.Google Scholar
  5. [5]
    Mandel L.: Phys. Rev.144 (1966), 1071.Google Scholar
  6. [6]
    Sudarshan E. C. G.: Phys. Rev. Let.10 (1963), 277.Google Scholar
  7. [7]
    Glauber R. J.: Quantum Optics and Electronics. (Ed. by C. DeWitt, A. Blandin, and C. Cohen-Tannoudji.) Gordon and Breach, New York 1965, pp. 65–185.Google Scholar
  8. [8]
    Ghielmetti F.: Phys. Let.12 (1964), 210.Google Scholar
  9. [9]
    Wolf E., Mehta C. L.: Phys. Rev. Let.13 (1964), 705.Google Scholar
  10. [10]
    PeŘina J.: Phys. Let.19 (1965), 195.Google Scholar
  11. [11]
    PeŘina J.: Czech. J. Phys.B 17 (1967), 1086.Google Scholar
  12. [12]
    Holliday D., Sage M. L.: Phys. Rev.138 (1965), B485.Google Scholar
  13. [13]
    Cahill K. E.: Phys. Rev.138 (1965), B1566.Google Scholar
  14. [14]
    Mehta C. L., Sudarshan E. C. G.: Phys. Rev.138 (1965), B274.Google Scholar
  15. [15]
    Klauder J. R., McKenna J., Currie D. G.: J. Math. Phys.6 (1965), 734.Google Scholar
  16. [16]
    Mandel L.: Phys. Rev.138 (1965), B753.Google Scholar
  17. [17]
    Lachs G.: Phys. Rev.138 (1965), B1012.Google Scholar
  18. [18]
    Glauber R. J.: Proceedings of the International Conference on the Physics of Quantum Electronics. (Ed. by P. L. Kelley, B. Lax and P. E. Tannenwald.) McGraw-Hill Book Co., New York 1965, p. 788.Google Scholar
  19. [19]
    PeŘina J.: Phys. Let.24A (1967), 333;24A (1967), 698; Acta Universitatis Palackianae (in press).Google Scholar
  20. [20]
    Troup G. J.: Proc. Phys. Soc.86 (1965), 39.Google Scholar

Copyright information

© Academia, Nakladatelství Československé akademie 1968

Authors and Affiliations

  • J. PeŘina
    • 1
  1. 1.Natural Science FacultyPalacký University, OlomoucOlomoucCzechoslovakia

Personalised recommendations