Using excited states and degeneracies to enhance the electric polarizability and first hyperpolarizability

We investigate the efficacy of boosting the nonlinear-optical response by using novel systems such as those in an excited state or with a degenerate ground state. By applying the three-level ansatz and using the Thomas Reiche-Kuhn sum rules as constraints, we find the electric polarizability and the first hyperpolarizability of excited-state systems to be bounded, but larger than those derived for a system in the ground state. It is shown that a system with a degenerate ground state can have divergent polarizabilities and that such divergences are real and not relics of a pathology in the perturbation theory. Furthermore, we demonstrate that these divergences occur only on time scales short compared with the relaxation time for the population difference to reach an equilibrium value. Such systems provide a way to obtain an ultra-large nonlinear-optical response. We discuss examples of huge enhancements in molecules and double quantum dots using a double quantum well as a model. (C) 2018 Optical Society of America