Abstract
The subject of spontaneous emission is a very old one. Recently this has received a whole new momentum because it has become possible to observe some of the peculiar phenomena associated with it. Of particular interest is the phenomenon of superradiance which was discovered by Dicke [1] in 1954. He found that the radiation rate from a collection of identical two-level atoms or molecules is, under certain circumstances depending on the excitation of the system, proportional to the square of the number of atoms. Dicke employed the second order perturbation theory to calculate the characteristics of the emitted radiation. We would, of course, like a description which enables us to calculate time dependent statistical properties.
Invited paper given at “Third Rochester Conference on Coherence and Quantum Optics”, June 21–23, 1972 Rochester, New York.
On leave of absence from the Department of Physics and Astronomy University of Rochester, Rochester, New York 14627
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Footnotes
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G.S. Agarwal Phys.Rev. A7 (1973)[in press]. Many of the results, which I would present here, have already appeared in these references.
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cf. ref. 13.
This part of our presentation follows closely ref. 10c.
The author would like to thank Dr. F. Haake for a discussion in which this point came up.
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Starting from a different viewpoint this master equation has also been obtained by Bonifacio etal, ref. 14. (a) Ω (2)ij , in principle, depends on the positions of ith and jth atom even for small systems. The permutation symmetry is also violated and it does not appear anymore convenient to work with the collective operators. However, there may be geometries for which Ω (2)ij ≈ Ω, i. e. it is on the average independent of i,j (cf. ref. 23). In such cases the solution (54) is modified to
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N.M. Kroll in Quantum Optics and Quantum Electronics ed. Cohen Tannoudji et al. (Gordon and Breach N.Y. 1965 ) p. 47.
cf. ref. (8); J.E. Walsch, Phys. Rev. Lett. 27, 208 (1971); G. Barton, Phys. Rev. A5, 468 (1972).
see e. g. ref. 12.
P.R. Fontana and D.J. Lynch, Phys. Rev. A2, 347 (1970).
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Agarwal, G.S. (1973). Master Equations in the Theory of Incoherent and Coherent Spontaneous Emission. In: Mandel, L., Wolf, E. (eds) Coherence and Quantum Optics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-2034-0_10
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