The critical role of the energy spectrum in determining the nonlinear-optical response of a quantum system

TL;DR

This paper investigates how the energy spectrum influences the nonlinear optical response of quantum systems, combining Monte Carlo and optimization methods to explain the gap between real molecules and theoretical limits.

Contribution

It introduces an energy spectrum constraint to unify Monte Carlo and optimization approaches, providing insights into the fundamental limits of hyperpolarizabilities.

Findings

Energy spectrum constrains hyperpolarizability responses

Explains the gap between molecules and fundamental limits

Supports the three-level ansatz hypothesis

Abstract

Studies aimed at understanding the global properties of the hyperpolarizabilities have focused on identifying universal properties when the hyperpolarizabilities are at the fundamental limit. These studies have taken two complimentary approaches: (1) Monte Carlo techniques that statistically probe the full parameter space of the Schrodinger Equation using the sum rules as a constraint; and, (2) numerical optimization studies of the first and second hyperpolarizability where models of the scalar and vector potentials are parameterized and the optimized parameters determined, from which universal properties are investigated. Here, we employ an energy spectrum constraint on the Monte Carlo method to bridge the divide between these two approaches. The results suggest an explanation for the origin of the factor of 20-30 gap between the best molecules and the fundamental limits and establishes the basis for the three-level ansatz.