Transition probabilities between quantum states of a molecular system interacting with a low intensity time dependent field were obtained. The molecular system is modeled as a quartic anhartnonic oscillator, whereas the interaction with the electric field is described by the electric-dipole approximation. We apply Lie algebraic techniques and make use of iterative Bogoliubov transformations (IBT) to derive an approximate expression for the evolution operator. The methodological procedure proposed by Yuen allows us to evaluate the final time evolution operator in a dosed form, using the optical properties of the two-photon coherent states of the radiation, field. © 2002 SPIE · 0277-786X/01/$15.00.