Theory of resonance excitation of N-level atomic systems by strong coherent radiation

Algebraic methods are developed for deriving steady-state solutions of the Bloch equations for a system of N atomic (molecular) levels resonantly coupled to strong coherent radiation fields in the rotating-wave approximation, and undergoing thermal (radiative and collisional) homogeneous relaxation. These methods are applied to a "ladder" model, in which the excitation and relaxation occur by one-level steps, with one field mode in resonance with each step. Explicit solution (in terms of coupling strengths, relaxation rates, and frequency detunings) is given for the three-level system, and some observations are made on systems of four or more levels. The process of solution of the N2-dimensional set of Bloch equations involves matrices of dimension N-1 or less.