  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.
