Exact Results for the Ionization of a Model Quantum System

We prove that a model atom having one bound state will be fully ionized by a time periodic potential of arbitrary strength r and frequency omega. Starting with the system in the bound state, the survival probability is for small r given by exp(-Gamma t) for times of order GAMMA^(-1)~r^(-2n) where n is the minimum number of 'photons' required for ionization (with large modifications at resonances). For late times the decay is as t^(-3) with the power law modulated by oscillations. As r increases, the time over which there is exponential decay becomes shorter and the power law behaviour starts earlier. Results are for a parametrically excited one-dimensional system with zero-range potential but comparison with analyticalworks and with experiments indicates that many features are general.