Exact Solutions for Many-Level Multiple-Resonance Problems

The matrix elements of the time-development operator are obtained exactly for the influence of many resonant or near-resonant fields on a system with a finite number of levels for arbitrary initial conditions in a wide class of problems. Perturbative techniques are presented which enable the exact treatment of all perturbations to a desired order. As examples, a three-level double-resonance and two eight-level triple-resonance systems are given. The applications of these exact solutions to the treatment of perturbations, including relaxation phenomena, are presented using both standard-perturbation-theory and density-matrix techniques.