By Donald L. Kreider, Robert G. Kuller, Donald R. Ostberg, Fred W. Perkins, Lynn H. LOoomis

An creation to Linear research

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They have been treated elegantly by F. T. Hioe and E. W. Montroll, 1. Math. PhI'S .. 16, 1259 (1975). 3. This is not true when (W. , - w) is very small. That is, when one of the states, U o or u" is almost degenerate with another optically connected state. We shall assume that it does not happen here but if it does one must then generalize to a multistate rotating wave approximation, 4. T. H. Einwohner. J, Wong, and J. C. Garrison. PhI'S. Rev. A. 14, 1452 (1976). 5, This is a perfectly legitimate form of A (I) but strictly speaking E(t) is then not the electric field amplitude.

Eberly, Wiley, New York, 1975, 2, These are the counterrotating terms which are the origin of the Bloch-Siegert shift: F. Bloch and A. J. F. Siegert, PhI'S. , 57. 522 (1940). They have been treated elegantly by F. T. Hioe and E. W. Montroll, 1. Math. PhI'S .. 16, 1259 (1975). 3. This is not true when (W. , - w) is very small. That is, when one of the states, U o or u" is almost degenerate with another optically connected state. We shall assume that it does not happen here but if it does one must then generalize to a multistate rotating wave approximation, 4.

Since typical a\1owed spontaneous decay times are of the order of 10- 8 sec, 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 then 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 I ones which use the density matrix and resort to ensemble averages for the description of the observations.

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