Coherence and Quantum Optics pp 273-288 | Cite as

# A Quantum Treatment of Spontaneous Emission Without Photons

## Abstract

The question whether it is possible to account for spontaneous emission of electromagnetic radiation from atoms without quantum electrodynamics has lately been the subject of further discussion.[1–5] In a recent article Nesbet[5] has considered an approach to the problem that differs substantially from the neoclassical approach of Jaynes and his co-workers.[1–3] In this theory the electromagnetic field is expressed explicitly in terms of its sources, which are quantized, and it obeys the algebra of the sources, while the concept of the free boson field is discarded altogether. Although he has referred to it as ‘semi-quantized radiation theory’, the theory is actually a fully quantized one, in the sense that no c-number currents or fields appear. When the rate of energy flow into the far electromagnetic field written in normal order is equated to the rate of energy loss of a two-level atom, Nesbet’s theory apparently leads to exponential decay of the atomic energy.[5,6]

## Keywords

Quantum System Spontaneous Emission Quantum Electrodynamic Poynting Vector Dimensional Hilbert Space## Preview

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## References

- 1.E.T. Jaynes and F.W. Cummings, Proc. IEEE
*51*, 89 (1963).CrossRefGoogle Scholar - 2.M.D. Crisp and E.T. Jaynes, Phys. Rev.
*179*, 1253 (1969).ADSCrossRefGoogle Scholar - 3.C.R. Stroud, Jr. and E.T. Jaynes, Phys. Rev.
*A1*, 106 (1970).ADSCrossRefGoogle Scholar - 4.R.K. Nesbet, Phys. Rev.
*A4*, 259 (1971).ADSCrossRefGoogle Scholar - 5.R.K. Nesbet, Phys. Rev. Letters
*27*, 553 (1971).ADSCrossRefGoogle Scholar - 6.A somewhat similar argument was implicit also in the work of N.E. Rehler and J.H. Eberly, Phys. Rev.
*A2*, 1735 (1971).Google Scholar - 7.J.S. Schwinger,
*Proceedings of the 1967 International Conference on Particles and Fields*, ed. C.R. Hagen, G. Guralnik and V.A. Mathur ( Interscience Publishers, John Wiley, New York, 1967 ) p. 128.Google Scholar - 8.W.L. Lama and L. Mandel, Phys. Rev.
*A6*, 2247 (1972).ADSCrossRefGoogle Scholar - 9.We label all Hilbert space operators by the caret.Google Scholar
- 10.L. Mandel, J. Opt. Soc. Am.
*62*, 1011 (1972).CrossRefGoogle Scholar - 11.See for example M. Born and E. Wolf,
*Principles of Optics, 4th Ed*. (Pergamon Press, Oxford, 1970) Section 2. 2. 3.Google Scholar - 12.We have recently been made aware of a treatment of the atomic decay problem by G.W. Series,
*Proceedings of the International Conference on Optical Pumping and Atomic Lineshape*, Warsaw, 1968, p. 25, in which the electromagnetic field is also expressed explicitly in terms of source operators, and the free field plays no role. By working with a larger Hilbert space, Series is able to derive both the decay rate and the Lamb shift.Google Scholar