Stimulated and spontaneous radiative frequency shifts of a two-level system

The quantum-electrodynamic frequency shifts of a two-level system in spontaneous emission and in an intense quantized radiation field are given up to eighth order in the coupling parameter, using the recursive perturbation method developed previously by one of the authors. The first six orders of the latter agree with the semiclassical result of Shirley and thus disagree with Chang and Stehle's calculation. The eighth-order term agrees with a recent semiclassical calculation by Ahmad and Bullough. The transition from the quantum mechanical case (the number of photons small) to the classical case (the number of photons very large) is also exhibited in our approach.