Maximization of the First Static Hyperpolarizability for a Finite Hermite Polynomial Sum Potential

Large nonlinear optical electronic polarizabilities would be advantageous for a variety of devices and have been intensely studied for around three decades. This project examines the theoretical limits on the static first non-linear electronic susceptibility of a material, known as the hyperpolarizability. Numerical optimizations for a single fermion in a one-dimensional potential suggest that the actual limit is about 71% of the analytically proven limit. Prior work by Joseph Lesnefsky for multiple noninteracting fermions in a peicewise linear potential suggests that in one dimension the ratio of numerically obtain hyperpolarizability to the analytical limit decreases with increasing number of non-interacting particles. We extended his work for the Hermite polynomial sum potentials to multiple fermions and compare the results to the piecewise linear potential case. From this new data, we examined the behavior of the resulting wave functions and dipole transition elements.