General solution to nonlinear optical quantum graphs using Dalgarno-Lewis summation techniques

TL;DR

This paper introduces a fast, ground-state-based algorithm using Dalgarno-Lewis perturbation theory to efficiently compute nonlinear optical properties of complex quantum graphs, outperforming traditional sum-over-states methods.

Contribution

The authors develop a general, efficient algorithm applying Dalgarno-Lewis theory to quantum graphs, significantly reducing computation time and complexity.

Findings

Replicates sum-over-states results with 10-50x speedup

Requires only ground state knowledge, simplifying calculations

Applicable to any quantum graph structure

Abstract

We develop an algorithm to apply the Dalgarno-Lewis (DL) perturbation theory to quantum graphs with multiple, connected edges. We use it to calculate the nonlinear optical hyperpolarizability tensors for graphs and show that it replicates the sum over states computations, but executes ten to fifty times faster. DL requires only knowledge of the ground state of the graph, eliminating the requirement to determine all possible degeneracies of a complex network. The algorithm is general and may be applied to any quantum graph.