Path-summation approach to the dynamics of radiative phenomena

We investigate a new form of the path-summation method, which is related to the Feynman-Vernon influence-functional approach, within a fairly standard model describing the two-level atom interacting with the (quantum) electromagnetic field. Our method, being essentially a nonperturbative one, is developed with perspective of application to dynamical problems, where the parameters of the (weak) atom-field interaction are combined with the parameters describing the (strong) pulse of radiation in the initial condition and/or in situations where one desires to calculate the time evolution of the field quantities. However, in this paper, after displaying the path-summation method in its general form, we test its possibilities just in the simplest case of populational-difference time evolution. The populational difference is formally expressed as a series in the level-splitting parameter. In the terms of this series, field averaging is explicitly performed and the physical analysis of the path contributions leads to a hierarchical class of nonperturbative partial-summation approximation based on the damping of the field correlations. We propose a trial form of the “correlation-damping” function, which enables the explicit discussion of the resulting time evolution. Finally, we compare the dynamics so obtained with the usual approach using the perturbative (in the atom-field interaction) expansion of the memory operator.