We calculate transition probabilities between discrete states of an anharmonic oscillator induced by a time dependent dipole. Our prototype oscillator includes a quadratic term n(2) in the quantum number n. The corresponding unperturbed Hamiltonian is expressed in terms of deformed ladder operators. To consider the perturbation due to the dipole interaction we introduce a dynamical mean field model Hamiltonian for the oscillator part. The resulting system is a parametric harmonic oscillator with a time dependent frequency determined self-consistently. We present results for the time dependence of transition probabilities for different pulses, as well as the expectation values of position and momentum. (C) 2011 Elsevier B. V. All rights reserved.