Abstract
When an atom is in a resonant laser field for a time that is long compared with the natural decay time of an excited state, then the probability that the state decays by emission of spontaneous photons into modes other than the laser mode must be included in our considerations. Since typical allowed spontaneous decay times are of the order of 10~8s, this is a common phenomenon. It is also a rather complicated phenomenon since in a typical experiment the atom may radiate (fluoresce) a thousand or so such photons. Thus, if we were to resort to a perturbation theory in the radiation operator, the theory would have to be carried to about the thousandth order. It is therefore necessary to have a technique for summing the important terms in the series. The existing theories fall into two categories: First there are the statistical ones1 which use the density matrix and resort to an ensemble average for the description of the observations. These lose nothing by their statistical nature since they describe the true state of affairs in which the entire state of the fluorescent field is never observed and so must be averaged. The second class are the so-called pure state theories2 which use wave functions and not density matrices and reserve sums over states for the last step. The latest versions of the two classes agree with each other and also have satisfactory agreement with experiment.3
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Notes and References
See, for example, M. Newstein, Phys. Rev. 167, 89 (1968), and J. R. Ackerhalt and J. H. Eberly, Phys. Rev. D 10, 3350 (1974), for two different approaches. For an excellent review see G. S. Agrawal, Quantum Statistical Theories of Spontaneous Emission and their Relation to Other Approaches, Springer-Verlag, Berlin (1974).
See, for example, S. Swain, J. Phys. A 8, 1277 (1975), and B. R. Mollow, Phys. Rev. A 12, 1919 (1975), for two different approaches of the pure state type.
F. Schuda, C. R. Stroud, Jr., and M. Hercher, J. Phys. B 7, L198 (1974);
A. M. Bonch-Bruevich, V. A. Khedovoi, and N. A. Chigir, Sov. Phys. JETP 40, 1027 (1975).
M. Ferray, A. L. L’Huillier, X. F. Li, L. A. Lompre, G. Mainfrey, and C. Manus, J. Phys. B 21, L31 (1988).
See, for example, L. I. Schiff, Quantum Mechanics, McGraw-Hill, New York (1968).
See the second of Ref. 2.
See, for example, A. I. Akhiezer and V. B. Berestetskii, Elements of Quantum Electrodynamics, Oldbourne Press, London (1962).
This equation, in various forms, has a long history in the literature; see, for example, the second and third of Ref. 1. It can be interpreted in a variety of ways but we choose to refer to it as a constraint on the wave function because it is local in time and because of its subsequent use to obtain (4.2.28). Equation (4.2.27) may also be obtained with higher accuracy. The additional terms on the right-hand side are of order γ/ ωL or ε/ ωL compared with those retained. They are always small.
M. L. Goldberger and K. M. Watson, Collision Theory, Wiley, New York (1964).
M. H. Mittleman and A. Tip, J. Phys. B 17, 571 (1984), and E. J. Robinson, Phys. Rev. A 33, 1461 (1986).
See any of Ref. 1.
This point has been emphasized in the discussion contained in the first of Ref. 2.
E. Fiordilino and M. H. Mittleman, J. Phys. B 17, 3037 (1984).
For an early review of the subject of optical pumping, see W. Happer, Rev. Mod. Phys. 44, 169 (1972). The experimental two-state atom is discussed in I. A. Abate, Opt. Commun. 10, 269 (1974), and E. Y. Fu, R. E. Grove, and S. Ezekiel, Phys. Rev. Lett. 35, 1426 (1975).
Antibunching of photons has been described by L. Mandel, J. Opt. (Paris) 10, 55 (1979).
This section is based on M. H. Mittleman, Phys. Rev. A 46, 4209 (1992), where a fuller description and the contribution of this effect to the width of these states are given.
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Mittleman, M.H. (1993). Spontaneous Radiation by Atoms in Lasers. In: Introduction to the Theory of Laser-Atom Interactions. Physics of Atoms and Molecules. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-2436-0_4
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