Monte Carlo Studies of the Intrinsic Second Hyperpolarizability

TL;DR

This study uses Monte Carlo simulations to explore the fundamental limits of the second hyperpolarizability, confirming that only three states dominate near the maximum, aligning with the three-level ansatz.

Contribution

It applies Monte Carlo methods to analyze the second hyperpolarizability's fundamental limit and confirms the three-level dominance near this limit.

Findings

Largest second hyperpolarizability values approach the fundamental limit.

Only three states dominate near the hyperpolarizability's upper bounds.

Results support the three-level ansatz for the second hyperpolarizability.

Abstract

The hyperpolarizability has been extensively studied to identify universal properties when it is near the fundamental limit. Here, we employ the Monte Carlo method to study the fundamental limit of the second hyperpolarizability. As was found for the hyperpolarizability, the largest values of the second hyperpolarizability approaches the calculated fundamental limit. The character of transition moments and energies of the energy eigenstates are investigated near the second hyperpolarizability's upper bounds using the missing state analysis, which assesses the role of each pair of states in their contribution. In agreement with the three-level ansatz, our results indicate that only three states (ground and two excited states) dominate when the second hyperpolarizability is near the limit.