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# Influence of Resonant Frequency Shifts on Superradiant Damping

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

## Abstract

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

## Keywords

Frequency Shift Identical Atom Shift Resonance Frequency Magnetostatic Interaction Entrance Face
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## References

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John David Jackson, Classical Electrodynamics (John Wiley and Sons, Inc., New York, London (1962)), p.271 Eq. (9.18).Google Scholar
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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).
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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)
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## 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