# Heralding pure single photons: a comparision between counter-propagating and co-propagating twin photons

## TL;DR

This paper compares counter-propagating and co-propagating geometries in spontaneous parametric down-conversion for generating high-purity heralded single photons, analyzing their efficiency and temporal entanglement.

## Contribution

It introduces a temporal domain correlation analysis to compare different photon generation strategies, highlighting the advantages of group-velocity matching.

## Key findings

- Counter-propagating geometry can produce high-purity photons.
- Group-velocity matching enhances heralded photon purity.
- Different strategies vary in efficiency and photon properties.

## Abstract

We investigate different strategies suitable to generate pure heralded single photons through spontaneous parametric down-conversion, comparing the counter-propagating geometry studied in [1] with more conventional co-propagating configurations which enhance the purity of the heralded photon state through the technique of group-velocity matching. Our analysis is based on the correlation of twin photons in the temporal domain,a non-standard approach that provides a physical view of the mechanisms that permit to eliminate the temporal entanglement of the state and to generate high-purity heralded photons. The Schmidt number associated to the temporal modes, which provides a more quantitative estimate of the purity, is then calculated. The efficiency of the various strategies and the individual properties of the heralded photons thereby generated are also compared.