Cooperative Phenomena in Resonant Propagation

  • E. Courtens
Conference paper


The cooperative emission of two atoms constrained to radiate along the line joining them can be calculated exactly. [1] One finds that for an atomic separation smaller than ∿ c/2γ the atoms radiate cooperatively, whereas for a greater separation they essentially radiate as if they were alone. This rather academic example can serve to introduce the notion of cooperation in resonant emission. The solution also emphasizes that a multi-mode quantum mechanical treatment is required to arrive at the proper answer. The notions of maximum cooperation time and maximum cooperation number, valid for a large assembly of radiating atoms, can however be arrived at on the basis of perturbation theory, provided a self-consistent argument is used. [1] The cooperation time fixes an upper limit to the duration of superradiant emission. It is the emission time when the superradiant system is essentially emitting in the absence of an applied field, as is the case for a “long” 2π-pulse, i.e., one for which the velocity of propagation v is much smaller than c/n. The maximum cooperation number is the maximum number of atoms that can possibly contribute to a coherent superradiant pulse.


Emission Time Cooperative Phenomenon Proper Answer Semiclassical Calculation Atomic Separation 
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    F.T. Arecchi and E. Courtens, Phys. Rev. 2A, 1730 (1970).ADSCrossRefGoogle Scholar
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    E. Courtens, in The Laser Handbook F.T. Arecchi and E.O. Shulz-Dubois, eds(North Holland Publ. Company),to appear in the fourth quarter of 1972, ch. E. 5, Section 5. 4.Google Scholar
  3. 3.
    N. Tan-no, K. Yokoto and H. Inaba, reported at the 7th International Quantum Electronics Conference, Montreal, Canada, May 1972, paper P. 7.Google Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • E. Courtens
    • 1
  1. 1.IBM Research LaboratoryZürichSwitzerland

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