Sequences of ultrafast non-resonant multiphoton transitions in a three-electronic level molecule

Non-resonant multiphoton transitions between three electronic states of a molecular system are studied. Based on a projection operator formalism which is formulated in the framework of the so-called time-local as well as the time-nonlocal approach, time-dependent Schrödinger equations are obtained, which include effective couplings to the laser field. For both procedures a slowly varying amplitude approximation can be invoked. The resulting time-local equations are solved in a much more efficient way than the original effective Schrödinger equations. The validity of these approximations is verified numerically for a two-photon process. Furthermore, the effective Schrödinger equations are specified to sequences of two-photon and three-photon transitions. The derived equations are applied to a molecular system consisting of three electronic states with Morse-type potential energy curves. Using different laser pulse scenarios the conditions are discussed under which a sequence of two-photon and three-photon transitions can take place.