# Entanglement properties of third harmonic generation via direct and cascaded parametric processes

## TL;DR

This paper compares two methods for generating third harmonic optical fields, analyzing their entanglement and EPR-steering properties in different configurations, revealing distinct advantages for each scheme.

## Contribution

It provides a comparative analysis of bipartite entanglement and EPR-steering in direct and cascaded third harmonic generation schemes, highlighting their respective strengths.

## Key findings

- Both schemes produce bipartite entanglement and EPR-steering.
- Direct scheme yields greater EPR-steering.
- Cascaded scheme offers more bipartition flexibility.

## Abstract

We compare the bipartite entanglement and EPR-steering properties of the two different schemes which produce third harmonic optical fields from an input field at the fundamental frequency. The first scheme uses second harmonic cascaded with sum-frequency generation while the second uses triply degenerate four-wave mixing, also known as direct third harmonic generation. We examine and compare the two schemes in both the travelling wave and intra-cavity configurations. We find that both schemes produce continuous-variable bipartite entanglement and EPR-steering. The direct scheme produces a greater degree of EPR-steering while the cascaded scheme allows for greater flexibility in having three available bipartitions.