# 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

## References

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)
4. 4.
V.M. Fain, Soviet Phys. JETP 36, 798 (1959).
5. 5.
R.H. Dicke, Phys. Rev. 93, 99 (1954).
6. 6.
F.T. Arecchi and D.M. Kim, Opt. Comm. 2, 324 (1970).
7. 7.
R. Plunder, Physica 28, 423 (1962).
8. 8.
R. Friedberg, S.R. Hartmann and J.T. Manassah, Phys. Letters 35A, 161 (1971).
9. 9.
R. Friedberg and S.R. Hartmann, Optics Comm. 2, 301 (1970).
10. 10.
C.R. Stroud, J.H. Eberly, W.L. Lama and L. Mandel, Phys. Rev. A5, 1094 (1972).
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).
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),
14. 14.
R. Bonifacio, P. Schwendimann and Fritz Haake, Phys. Rev. A4, 854 (1971).
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

© 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