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 (TLA) and using the Thomas-Reiche-Kuhn (TRK) sum rules as constraints, we find the electric polarizability and 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 intrinsic polarizabilities and that such divergences are real and not relics of a pathology in the perturbation theory. Furthermore, we demonstrate that these divergences only occur on time scales short compared to the relaxation time of the population difference to an equilibrium value. Such systems provide a way to get 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.