Dipole induced transitions in an anharmonic oscillator: A dynamical mean field model

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.