Continued fraction perturbation theory: applications to radiative processes in the dipole approximation

Abstract

A general perturbation procedure is described for writing down the contributions to any order for the probability of a quantum system described by a time-independent Hamiltonian making a transition from an arbitrary initial state to an arbitrary final state. The results are expressed in terms of certain propagators which involve continued fractions, so that some processes are summed to all orders. The general theory is then applied to a single multilevel atom interacting with any number of modes of the electromagnetic field in the electric dipole approximation. The fundamental theory is considered primarily but a detailed discussion is given of spontaneous and stimulated emission. Expressions for the lineshape are derived incorporating the generalized Lamb shifts and damping constants.