Beyond Planck-Einstein quanta: amplitude driven quantum excitation

Linear-response quantum excitation is proportional to the amplitude of the field, with the energy of the excitation given by the driving frequency. As the amplitude is increased, there is a crossover, where the excitation energy is governed by the amplitude of the driving field, not its frequency. As the amplitude is increased even further, then complex quantum oscillations develop, whose origin is related to Wannier-Stark physics, but has no simple explanation. We illustrate this phenomena with the exact solution of the simplest model of a charge-density-wave insulator driven by a uniform time-dependent electric field.