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By P. L. Knight, L. Allen
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Additional info for Concepts of Quantum Optics
16) is ^f ( t) = x d 2 l eg! £ d t '£ d t " e^g(t"-t') ^ l E ^ ' c f )|HifX*f | 2 H" . 17) over all possible final states |^f> accessible from |i|/j> by one-photon absorption. 18) We see immediately that the excitation is determined by a field correlation function. 18) can be removed if we consider an idealised broadband detector for our attention. Many final states with a range of energies much wider than the bandwidth of the radiation field contribute to the absorption otherwise the detector would only see certain Fourier components and not respond to others; the energy range is also much wider than ( 4 Coherence Functions 48 the reciprocal of the detection time, t"^.
Sargent, Scully and Lamb 1974; Durrant, Reprinted Paper 10). For atoms initially in their excited state however, the dipoles give rise to a field which constructively interferes in the forward direction to give amplification rather than absorption of the incident field. Imagine an incident field W E ( r , t ) = e EQcos(u)t - k. 68) where z is the1 unit polarization vector. This field interacts with an atom at position r at time t through the coupling W ? E (r ,t). 69) At time t, the wavefunction of our two-level system made up of states |f>and |i>is, from eqs.
56). 57) is made we recognise that there is no difference between semiclassical and fully-quantized treatments of weak field absorption. This remains true when the state |b> (or |f> in semiclassical theory) is replaced by a large number of accessible final states. Consequently a quantized field treatment is not necessary for*a proper understanding of the photoelectric effect. A semiclassical discussion of which, based on first order perturbation theory and formulated in a similar manner to our discussion, is given in the Reprinted Paper 9 by Mandel, Sudarshan and Wolf.