Application of the magnus expansion for high-order multiphoton excitation

In this paper we present the results of a study of the multiphoton dynamics of a truncated Morse oscillator, calculating the dependence of the dissociation probability from the uppermost level and of the mean vibrational excitation energy on the intensity and the frequency of the electromagnetic field. These calculations were performed for several forms of the dipole moment operator, involving linear and exponential dipole functions. These calculations establish the validity range of the rotating wave approximation (RWA), which allows the use of the effective hamiltonian formalism to treat the dynamics. The calculations demonstrate the applicability of the Magnus expansion to the multiphoton excitation of a sparse level system for which the RWA is not applicable. This work also establishes two effects of the form of the dipole moment operator on multiphoton excitation of the oscillator. These involve the possibility of the occurrence of bottlenecks in the radiative coupling matrix elements, which reduce the efficiency of multiphoton excitation and the presence of radiative coupling between nonadjacent energy levels, which greatly enhance the efficiency of excitation. Both of these effects can lead to the breakdown of the RWA, even for moderately small multilevel systems.