Generalized two phonon theory

Recent laser experiments and theoretical discussions of coherent two photon transient phenomena have prompted us to develop a generalized theory for the case of anN+2 level quantum system interacting with two optical fields. New perturbation solutions, derived from an effective two level Hamiltonian, are presented in the form of a continued fraction expansion where the leading term agrees with earlier treatments. The theory applies to homogeneously broadened systems where the intermediate transitions are far off resonance. When inhomogeneous broadening plays a role, the expansion parameter is no longer unique and the theory breaks down. Nonperturbative solutions are then required which are also capable of explaining other features not appearing in the perturbative approach. An important example is intensity-dependent dephasing. Exact and approximate solutions of this kind are derived.