Nonlinear sum rules: The three-level and the anharmonic-oscillator models

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Abstract
Recently derived sum rules for nonlinear optics are shown to be relevant to a number of experiments in atomic and solid-state physics. To interpret the experiments on atomic transitions and exciton transitions in solids, we analyze the three-level model and examine the modification of the optical spectrum induced on a probe light by the presence of an additional intense light beam. We show that the nonlinear sum rules explain the known experimental data and predict anomalous asymmetry in the nonlinear line shape. We also consider the cases of vibrational states of diatomic molecules and of optical modes of polar crystals and treat them with the model of the anharmonic oscillator. The nonlinear sum rules are shown to be obeyed, thus clarifying the processes of nonlinear absorption.