Universal properties of the optimized off-resonant intrinsic second hyperpolarizability

Abstract

We seek to identify universal properties shared by all quantum systems with large intrinsic second hyperpolarizability (γint)—an invariant quantity that removes the effects of simple scaling. A large-γint quantum system is generated by varying the shape of a trial potential until γint is optimized. A variety of starting potentials yield a set of systems with distinctly shaped optimized potentials, but are found to share universal properties that separate into classes determined by the magnitude and sign of γint. However, the fact that the best systems are 0.6 times the fundamental limit suggests that exotic Hamiltonians may be required to reach the upper bound. The observed regularity hints at a deeper relationship between optimized systems that may provide useful insights applicable to designing better materials. Being general, this approach applies to any quantum system, including molecules, nanoparticles, or quantum gases.