Dressed quantum graphs with optical nonlinearities approaching the fundamental limit

TL;DR

This paper introduces dressed quantum graphs with finite delta potentials that optimize optical nonlinearities near fundamental limits, revealing new insights into the state requirements and scaling properties of such systems.

Contribution

It presents the first analytical model of dressed quantum graphs with nonlinear optical responses approaching fundamental limits, highlighting the role of finite potentials and eigenfunction shape optimization.

Findings

Structures with near-maximum hyperpolarizability are described by three states.

Largest second hyperpolarizability requires four states.

An exception to universal scaling is linked to eigenfunction discontinuities.

Abstract

We dress bare quantum graphs with finite delta function potentials and calculate optical nonlinearities that are found to match the fundamental limits set by potential optimization. We show that structures whose first hyperpolarizability is near the maximum are well described by only three states, the so-called three-level Ansatz, while structures with the largest second hyperpolarizability require four states. We analyze a very large set of configurations for graphs with quasi-quadratic energy spectra and show how they exhibit better response than bare graphs through exquisite optimization of the shape of the eigenfunctions enabled by the existence of the finite potentials. We also discover an exception to the universal scaling properties of the three-level model parameters and trace it to the observation that a greater number of levels are required to satisfy the sum rules even when the three-level Ansatz is satisfied and the first hyperpolarizability is at its maximum value, as specified by potential optimization. This exception in the universal scaling properties of nonlinear optical structures at the limit is traced to the discontinuity in the gradient of the eigenfunctions at the location of the delta potential. This is the first time that dressed quantum graphs have been devised and solved for their nonlinear response, and it is the first analytical model of a confined dynamic system with a simple potential energy that achieves the fundamental limits.