Harmonium in intense laser fields: excitation, absorption, and transparency

It is known that the dynamics of two (Coulomb-interacting) nonrelativistic electrons confined by a parabolic potential and driven by a classical, intense laser field (in dipole approximation) is exactly soluble. We calculate the time-dependent population of the harmonic oscillator states and the energy absorbed from the laser. It turns out that the key entity on which all observables sensitively depends is the modulus square of the Fourier-transformed vector potential of the laser field, evaluated at the harmonic oscillator frequency. The system is transparent to laser field configurations for which this entity vanishes. We discuss the Poisson statistics behavior of the transition probabilities and analyze the conditions for the complete survival and full depletion of the initial state.