Summation of four-operator perturbation series: Application to atom-atom intensity-dependent correlations.

Abstract

It is shown how certain classes of problems dealing with the interaction of radiation with atoms can be formulated in terms of four-operator perturbation series. The case of an isolated atom coupled to a single-mode field is discussed in detail within the resolvent formalism. The process where no photon is effectively absorbed by the atom is described, to all orders, in terms of a series involving four operators which simultaneously increase and/or decrease the photon number and the orbital quantum number. This series is exactly summed and the summation technique is generalized to single-atom, two-field and to two-atom, single-field systems exhibiting zero, one, and two net photon absorptions or emissions. The theory is applied to induced emission of a single photon from a pair of two-level atoms coupled to a monomode radiation field. The energy diagrams, the time dependence of the probability, and the resonance curves are discussed for systems where (i) both atoms are in the upper state and (ii) atom 1 is in the upper state and atom 2 is in the lower state at t=0. In comparing these results to the ones obtained with a single atom, we find that the important intensity-dependent correlations give rise to trapping effects even when the atoms are initially in the upper state.