Superradiance from a System of 3-Level Particles

  • Y. C. Cho
  • N. A. Kurnit
  • R. Gilmore


Superradiance, first discussed in 1954 by Dicke [1], has recently re-emerged as one of the central interests in the field of atomic radiation, due in part to experimental developments in the area of short pulse coherent interactions [2],[3].


Single Particle State Symmetric Representation Bloch State Semiclassical Treatment Single Particle Energy Level 
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  1. 1.
    R.H. Dicke, Phys. Rev. 93, 99 (1954).ADSMATHCrossRefGoogle Scholar
  2. 2.
    I.D. Abella, N.A. Kurnit and S.R. Hartmann, Phys. Rev. 141, 391 (1966).ADSCrossRefGoogle Scholar
  3. 3.
    S.L. McCall and E.L. Hahn, Phys. Rev. 183, 457 (1969).ADSCrossRefGoogle Scholar
  4. 4.
    F.T. Arecchi and E. Courtens, Phys. Rev. A2, 1730 (1970).ADSCrossRefGoogle Scholar
  5. 5.
    F. Bloch, Phys. Rev. 70, 460 (1946).ADSCrossRefGoogle Scholar
  6. 6a.
    G. Racah, Ergeb. Exakt. Naturw. 37, 28 (1965).MathSciNetGoogle Scholar
  7. b.
    E.M. Loebl, Group Theory (Academic Press, 1968 ).MATHGoogle Scholar
  8. c.
    c. M. Hamermesh, Group Theory (Addison-Wesley Co., 1962 ).MATHGoogle Scholar
  9. d.
    H.J. Lipkin, Lie Groups (North Holland Pub.Co., Amsterdam, 1966 ).MATHGoogle Scholar
  10. e.
    R. Gilmore, J. of Math. Phys. 11, 513 and 3420 (1970).MathSciNetADSMATHCrossRefGoogle Scholar
  11. 7.
    This approach has been suggested by F.T. Arecchi and D.M. Kim, who collaborated with one of us (R.G.) on preliminary investigations. See also L.A. Shelepin, Zh. Eksp. Theor. Fiz. 54, 1463 (1968) (Sov. Phys. JETP 27, 784 (1968)).Google Scholar
  12. 8.
    Y.C. Cho, Ph.D. Thesis, M.I.T. (1972) (unpublished).Google Scholar
  13. 9.
    We assume here that ω1, ω2 and ω3 are different from one another to the limits of the superradiant line breadth so that interference may be avoided.Google Scholar
  14. 10.
    See p. 187 in Ref. 6(b).Google Scholar
  15. 11.
    The classification into irreducible representations is illustrated for four three-level particles in Fig. 4 of the paper by R. Gilmore in this volume, p. 217.Google Scholar
  16. 12.
    Eigenvalues of H1 and H2 are called weights of the representation of SU(3). In this paper, each weight is subtracted by the lowest weight so that the collective ground state is redefined as zero energy level.Google Scholar
  17. 13.
    R. Bonifacio, D.M. Kim and M.O. Scully, Phys. Rev. 187, 441 (1969).ADSCrossRefGoogle Scholar
  18. 14.
    R. H. Dicke, Quantum Electronics III (N. Bloembergen and P. Grivet, eds., 1964), vol. 1, p. 35. See also Refs. 1, 15 and 16.Google Scholar
  19. 15.
    N.E. Rehler and J.H. Eberly, Phys. Rev. A3, 1735 (1971).MathSciNetADSCrossRefGoogle Scholar
  20. 16.
    R. Bonifacio and P. Schwendimann, Nuovo Cimento Letters 3, 509 (1970). See also R. Bonifacio, P. Schwendimann and F. Haake, Phys. Rev. A4, 302 and 854 (1971).CrossRefGoogle Scholar
  21. 17.
    See also R. Friedberg and S.R. Hartmann, Physics Letters 37A, 285 (1971).CrossRefGoogle Scholar
  22. 18.
    The permutational invariance of the interaction can be maintained even for low mirror reflectivity by assuming, for example, a traveling wave ring laser cavity with distributed losses.Google Scholar
  23. 19.
    See Appendix G in Ref. 2. As discussed here and in Ref. 15, this result pertains to a sample with a large Fresnel number.Google Scholar
  24. 20.
    Similar differential equations, but without the constant η which accounts for quantum fluctuations, have been derived by M.D. Crisp and E.T. Jaynes, Phys. Rev. 179, 1253 (1969), using a semiclassical treatment.ADSCrossRefGoogle Scholar
  25. 21.
    The proceeding discussions can be extended to the case γ2≠0.Google Scholar
  26. 22.
    If (X0, Y0)∼ η, the quantum fluctuation would be so large during spontaneous decay that the semiclassical treatment would result in considerable error.Google Scholar
  27. 23.
    It must be emphasized that the interference between the γ1 transition and the γ2 transition should have been taken into account for λ1= 2λ312) if γ2 were not assumed to be zero.Google Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Y. C. Cho
    • 1
  • N. A. Kurnit
    • 1
  • R. Gilmore
    • 2
  1. 1.Massachusetts Institute of TechnologyCambridgeUSA
  2. 2.University of Southern FloridaTampaUSA

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