Coupled Superradiance Master Equations: Application to Fluctuations in Coherent Pulse Propagation in Resonant Media

  • Charles R. Willis
  • R. H. Picard
Conference paper


Cooperative phenomena in radiation-matter interactions range from coherent pulse propagation on the one hand to superradiant emission on the other. The question of fluctuations in cooperative phenomena has received little consideration despite its importance both for stability studies of pulse propagation and for elucidating the connection between superradiance and pulse propagation. The usual procedure is to treat coherent pulse propagation and super-radiance as completely different problems in spite of the fact that the interaction Hamiltonian is the same and the effects proportional to N2 dominate in both cases. One of the main purposes of this paper is to present and discuss the results of a master-equation formalism that provides a unified treatment of coherent pulse propagation and fluctuation phenomena by splitting off and treating exactly the self-consistent part of the matter-field interaction. A second main purpose of the paper is to show how easily one may generalize existing formulations of the superradiance problem by treating dynamically the radiation field, as well as the matter,thus leading to a system of two coupled master equations for the reduced density operators of the matter and of the field.


Master Equation Cooperative Phenomenon Reduce Density Operator Coherent Propagation Field Moment 
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.

Footnotes and References

  1. 1.
    S.L. McCall and E.L. Hahn, Phys. Rev. 183, 457 (1969).ADSCrossRefGoogle Scholar
  2. G.L. Lamb Jr., Rev. Mod. Phys. 43, 99 (1971).MathSciNetADSCrossRefGoogle Scholar
  3. 2.
    C.R. Willis, J. Math. Phys. 5, 1241 (1964).MathSciNetADSCrossRefGoogle Scholar
  4. 3.
    R.H. Dicke, Phys. Rev. 93, 99 (1954).ADSMATHCrossRefGoogle Scholar
  5. 4.
    V.M. Fain and Ya. I. Khanin, Quantum Electronics (MIT Press, Cambridge, Mass., 1969 ).Google Scholar
  6. 5.
    V. Ernst and P. Stehle, Phys. Rev. 176, 1456 (1968).ADSCrossRefGoogle Scholar
  7. 6.
    N.E. Rehler and J.H. Eberly, Phys. Rev. A3, 1735 (1971).MathSciNetADSCrossRefGoogle Scholar
  8. 7.
    G.S. Agarwal, Phys. Rev. A2, 2038 (1970); A4, 1783 (1971); A4, 1791 (1971).Google Scholar
  9. 8.
    R. Bonifacio, P. Schwendimann and F. Haake, Phys. Rev. A4, 302 (1971) and Phys. Rev. A4, 854 (1971).ADSGoogle Scholar
  10. 9.
    F. Haake and R.J. Glauber, Phys. Rev. A5, 1457 (1971).Google Scholar
  11. 10.
    Instead they obtain a small parameter e by giving the photons a finite lifetime in the cavity equal to the one-way transit time, τint =L/c and choosing τrel ≡ (μ2NL/c)−1 where μ is the atom-field coupling constant defined in Eq. (4).Google Scholar
  12. 11.
    R.H. Picard, Ph.D. Thesis, Boston University (1968).Google Scholar
  13. 12.
    N.N. Bogoliubov in Studies in Statistical Mechanics, edited by J. deBoer and G.E. Uhlenbeck ( North Holland Publishing Co., Amsterdam, 1962 ) pp. 5–118.Google Scholar
  14. 13.
    Our operators Pk+ are identical with Dicke’s operators Rk± in ref. 3.Google Scholar
  15. 14.
    R.H. Zwanzig, Physica 30, 1109 (1964).MathSciNetADSCrossRefGoogle Scholar
  16. 15.
    R.H. Picard and C.R. Willis, Phys. Letters 37A, 301 (1971).ADSCrossRefGoogle Scholar
  17. 16.
    R.J. Glauber, Phys. Rev. 131, 2766 (1963). The weight function is denoted by P({αk}) in this reference.MathSciNetADSCrossRefGoogle Scholar
  18. 17.
    F.A. Hopf and M.O. Scully, Phys. Rev. 179, 399 (1969).ADSCrossRefGoogle Scholar
  19. 18.
    F.T. Arecchi and R. Bonifacio, IEEE J. quantum Electron, 1, 169 (1965).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Charles R. Willis
    • 1
  • R. H. Picard
    • 2
  1. 1.Boston UniversityBostonUSA
  2. 2.Air Force Cambridge Research LaboratoriesBedfordUSA

Personalised recommendations