Advertisement

Master Equations in the Theory of Incoherent and Coherent Spontaneous Emission

  • G. S. Agarwal
Conference paper

Abstract

The subject of spontaneous emission is a very old one. Recently this has received a whole new momentum because it has become possible to observe some of the peculiar phenomena associated with it. Of particular interest is the phenomenon of superradiance which was discovered by Dicke [1] in 1954. He found that the radiation rate from a collection of identical two-level atoms or molecules is, under certain circumstances depending on the excitation of the system, proportional to the square of the number of atoms. Dicke employed the second order perturbation theory to calculate the characteristics of the emitted radiation. We would, of course, like a description which enables us to calculate time dependent statistical properties.

Keywords

Master Equation Spontaneous Emission Atomic System Black Body Radiation Radiation Rate 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Footnotes

  1. 1.
    R.H. Dicke, Phys. Rev. 93, 99 (1954).ADSMATHCrossRefGoogle Scholar
  2. 2.
    V. Weisskopf and E. Wigner, Z. Physik 63, 54 (1930), ibid., 65 18 (1931).ADSCrossRefGoogle Scholar
  3. 3.
    V. Weisskopf, Ann. Physik 9, 23 (1931), Z. Physik 85, 451 (1933).Google Scholar
  4. 4.
    W. Heitler and S.T. Ma, Proc. Roy. Ir. Ac. 52, 109 (1949); W. Heitler Quantum Theory of Radiation(Oxford University Press, 3rd edition) § 16.MathSciNetGoogle Scholar
  5. 5.
    M.L. Goldberger and K.M. Watson Collision Theory (John Wiley New York, 1964), Chapter 8: Generalizations of this method are given in A.S. Goldhaber and K.M. Watson, Phys. Rev.160, 1151 (1967); L. Mower, Phys. Rev. 165, 145 (1968).MATHGoogle Scholar
  6. 6.
    F.E. Low, Phys. Rev. 88, 53 (1952).ADSMATHCrossRefGoogle Scholar
  7. 7.
    E.T. Jaynes and F.W. Cummings, Proc.IEEE 51, 89 (1963); M.D. Crisp and E.T. Jaynes, Phys. Rev.179, 1253 (1969); C.R. Stroud and E.T. Jaynes, Phys. Rev. A1, 106 (1970)CrossRefGoogle Scholar
  8. 8.
    C.S. Chang and P. Stehle, Phys. Rev. A4, 641 (1971).ADSCrossRefGoogle Scholar
  9. 9.
    M.Dillard and H.R. Robl, Phys. Rev. 184, 312 (1969).ADSCrossRefGoogle Scholar
  10. 10(a).
    G.S. Agarwal Phys. Rev. A2, 2038 (1970).ADSCrossRefGoogle Scholar
  11. 10(b).
    G.S. Agarwal Phys. Rev. A3, 1783 (1971);ADSGoogle Scholar
  12. 10(c).
    G.S. Agarwal Nuovo Cim. Lett. 2, 49 (1971);Google Scholar
  13. 10(d).
    G.S. Agarwal Nuovo Cim. Lett. 2, 49 (1971);Google Scholar
  14. 10(e).
    G.S. Agarwal Phys. Rev. A4, 1778 (1971);ADSGoogle Scholar
  15. 10(f).
    G.S. Agarwal Phys.Rev. A7 (1973)[in press]. Many of the results, which I would present here, have already appeared in these references.Google Scholar
  16. 11.
    R.W. Zwanzig in Lectures in Theoretical Physics, ed. W.E. Brit- tin et al (Wiley, New York 1961) Vol. Ill; Physica 33, 119 (1964); see also G.S. Agarwal, Phys. Rev. 178, 2025 (1969).Google Scholar
  17. 12.
    For the use of such methods to other problems in quantum optics, we refer to G.S. Agarwal in Progress in Optics, ed. E. Wolf (North-Holland Publ. Co., Amsterdam) Vol. XI (in press).Google Scholar
  18. 13.
    R.H. Lehmberg, Phys. Rev. A2, 883 (1970); ibid A2, 889 (1970).ADSGoogle Scholar
  19. 14.
    R. Bonifacio, P. Schwendimann and F. Haake, Phys. Rev. A4, 302 (1971); ibid A4, 854 (1971); R. Bonifacio and P. Schwendimann, Nuovo Cim. Letters 3, 512 (1970).Google Scholar
  20. 15.
    See e. g. H. Haken in Handbuch der Physik ed. S. Flügge (Springer, Berlin 1970), Vol. XXV/2c, p. 28.Google Scholar
  21. 16.
    See e. g. E.A. Power and S. Zienau, Phil. Trans. Roy. Soc. 251, 427 (1959).MathSciNetADSMATHCrossRefGoogle Scholar
  22. 17.
    E.A. Power, Nuovo Cim 6, 7 (1957); M.J. Stephen, J. Chem. Phys. 40, 669 (1964).MathSciNetMATHCrossRefGoogle Scholar
  23. 18.
    M. Lax, Phys. Rev. 172, 350 (1968),ADSCrossRefGoogle Scholar
  24. 19.
    J.H. Eberly and N.E. Rehler,Phys. Lett. 29A, 142 (1969); N.E. Rehler and J.H. Eberly,Phys. Rev. A3, 1735 (1971).Google Scholar
  25. 20.
    cf. ref. 13.Google Scholar
  26. 21.
    This part of our presentation follows closely ref. 10c.Google Scholar
  27. 22.
    The author would like to thank Dr. F. Haake for a discussion in which this point came up.Google Scholar
  28. 23.
    C.R. Stroud, J.H. Eberly, W.L. Lama and L. Mandel, Phys. Rev. A5, 1094 (1971).Google Scholar
  29. 24.
    F.T. Arecchi, G.P. Banfi and V. Fassato-Bellani, Nuovo Cim. (in print).Google Scholar
  30. 25.
    E.C.G. Sudarshan, Phys. Rev. Letters 10, 277 (1965); R. J. Glauber, Phys. R. v.131,2766 (1963). For the general transformation of the operator equations into c-number equations, see G.S. Agarwal and E. Wolf, Phys. Rev. Lett. 21, 180 (1968); Phys. Rev. D2, 2187 (1970).MathSciNetADSCrossRefGoogle Scholar
  31. 26.
    W.L. Lama, R. Jodoin and L. Mandel, Am. J. Phys. 40, 32 (1972).ADSCrossRefGoogle Scholar
  32. 27.
    Starting from a different viewpoint this master equation has also been obtained by Bonifacio etal, ref. 14. (a) Ωij(2), in principle, depends on the positions of ith and jth atom even for small systems. The permutation symmetry is also violated and it does not appear anymore convenient to work with the collective operators. However, there may be geometries for which Ωij(2) ≈ Ω, i. e. it is on the average independent of i,j (cf. ref. 23). In such cases the solution (54) is modified toGoogle Scholar
  33. 28.
    A.M. Ponte Goncalves and A. Tallet, Phys. Rev. A4, 1319 (1971).ADSCrossRefGoogle Scholar
  34. 29.
    Such decoupling procedures are, of course, very familiar in non-equilibrium statistical mechanics, see e. g. D.N. Zubarev, Sov. Phys. Uspekhi 3, 320 (1960); see also L.P. Kadanoff and G. Baym Quantum Statistical Mechanics ( Benjamin Inc., New York 1962 ).MathSciNetADSCrossRefGoogle Scholar
  35. 30.
    R. Bonifacio and M. Gronchi, Nuovo Cim. Lett.1, 1105 (1971); V. DeGiorgio, Opt. Commun. 2, 362 (1971).CrossRefGoogle Scholar
  36. 31.
    N.M. Kroll in Quantum Optics and Quantum Electronics ed. Cohen Tannoudji et al. (Gordon and Breach N.Y. 1965 ) p. 47.Google Scholar
  37. 32.
    cf. ref. (8); J.E. Walsch, Phys. Rev. Lett. 27, 208 (1971); G. Barton, Phys. Rev. A5, 468 (1972).CrossRefGoogle Scholar
  38. 33.
    see e. g. ref. 12.Google Scholar
  39. 34.
    P.R. Fontana and D.J. Lynch, Phys. Rev. A2, 347 (1970).ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • G. S. Agarwal
    • 1
  1. 1.Universität StuttgartStuttgartGermany

Personalised recommendations