A nonperturbative approach to induced transitions between atomic states by weak electromagnetic waves

Abstract

We restudy the transitions between atomic states induced by electromagnetic waves (absorption or induced emission) of ordinary optical sources. Though the electromagnetic field is weak in this case, the result of standard treatment by time-dependent perturbation theory is obviously unreasonable in the near resonant region. In spite of the continuous developments of nonperturbative methods for relevant subjects, an explicit nonperturbative solution still seems not available. We present a nonperturbative approach to the problem for near resonant fields and give an explicit solution, albeit approximate. All transition probabilities take Rabi oscillation forms involving several frequencies. Under the perturbation condition our results reduce to those of perturbation theory. In the general results, the electric-dipole selection rules are approximately recovered only for short time. For large time, however, probabilities for forbidden transitions may become comparable with those for allowed ones.