Influence of Resonant Frequency Shifts on Superradiant Damping

  • R. Friedberg
  • S. R. Hartmann
  • Jamal T. Manassah
Conference paper


The interaction between two electric dipoles p 1 and p 2 at position r 1 and r 2, analyzed at frequency kc, is [1]
$$\begin{array}{l} v = - {e^{ikr}}[\left( {{{\vec p}_1} \cdot {{\vec p}_2} - \hat r \cdot {{\vec p}_1}\,\hat r \cdot {{\vec p}_2}} \right)\frac{{{k^2}}}{r}\\ + \left( {{{\vec p}_1} \cdot {{\vec p}_2} - 3\hat r \cdot {{\vec p}_1}\,\hat r \cdot {{\vec p}_2}} \right)\left( {\frac{{ik}}{{{r^2}}} - \frac{1}{{{r^3}}}} \right)]\\ = \frac{1}{{{r^3}}}\left( {{{\vec p}_1} \cdot {{\vec p}_2} - 3\hat r \cdot {{\vec p}_1}\,\hat r \cdot {{\vec p}_2}} \right) - \frac{{{k^2}}}{{2r}}\left( {{{\vec p}_1} \cdot {{\vec p}_2} - \hat r \cdot {{\vec p}_1}\,\hat r \cdot {{\vec p}_2}} \right)\\ - \frac{2}{3}\,i\,{k^3}\,{{\vec p}_1} \cdot {{\vec p}_2} + 0\left[ r \right]\\ where\,{{\vec r}_1} - {{\vec r}_2} = r\hat r. \end{array}$$


Frequency Shift Identical Atom Shift Resonance Frequency Magnetostatic Interaction Entrance Face 
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  1. 1.
    John David Jackson, Classical Electrodynamics (John Wiley and Sons, Inc., New York, London (1962)), p.271 Eq. (9.18).Google Scholar
  2. 2.
    H.A. Lorentz, Theory of Electrons (Dover, New York, 2nd Ed., (1952)).Google Scholar
  3. 3.
    C. Kittel, Phys. Rev. 73, 155 (1948)ADSCrossRefGoogle Scholar
  4. 4.
    V.M. Fain, Soviet Phys. JETP 36, 798 (1959).MathSciNetGoogle Scholar
  5. 5.
    R.H. Dicke, Phys. Rev. 93, 99 (1954).ADSMATHCrossRefGoogle Scholar
  6. 6.
    F.T. Arecchi and D.M. Kim, Opt. Comm. 2, 324 (1970).ADSCrossRefGoogle Scholar
  7. 7.
    R. Plunder, Physica 28, 423 (1962).ADSCrossRefGoogle Scholar
  8. 8.
    R. Friedberg, S.R. Hartmann and J.T. Manassah, Phys. Letters 35A, 161 (1971).ADSCrossRefGoogle Scholar
  9. 9.
    R. Friedberg and S.R. Hartmann, Optics Comm. 2, 301 (1970).ADSCrossRefGoogle Scholar
  10. 10.
    C.R. Stroud, J.H. Eberly, W.L. Lama and L. Mandel, Phys. Rev. A5, 1094 (1972).ADSCrossRefGoogle Scholar
  11. 11.
    An explicit formula for the dephasing time can be found in R. Friedberg, S.R. Hartmann and Jamal T. Manassah, Phys. Letters 40A, 365 (1972).ADSCrossRefGoogle Scholar
  12. 12.
    F.T. Arecchi and Eric Courtens, Phys. Rev. A2, 1730 (1971).Google Scholar
  13. 13.
    N.E. Rehler and J.H. Eberly, Phys. Rev. A3, 1735 (1971),MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    R. Bonifacio, P. Schwendimann and Fritz Haake, Phys. Rev. A4, 854 (1971).ADSGoogle Scholar
  15. 15.(a)
    For examples from this conference we cite Kenneth G, Whitney: “A Quantum Electrodynamic View of Superradiance as a Competition between Stimulated and Spontaneous Atomic Decay”.Google Scholar
  16. 15.(b)
    G.S. Agarwal: “Master Equations in the Theory of Incoherent and Coherent Spontaneous EmissionGoogle Scholar
  17. 15.(c)
    R.K. Bullough: “Nonlinear Radiation Reaction”(a) p. 767,(b) p. 157, (c) p. 121, this volumeGoogle Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • R. Friedberg
    • 1
  • S. R. Hartmann
    • 1
  • Jamal T. Manassah
    • 2
    • 1
  1. 1.Columbia UniversityNew YorkUSA
  2. 2.Institute for Advanced StudyPrincetonUSA

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