Disclosing the spatio-temporal structure of PDC entanglement through frequency up-conversion

TL;DR

This paper presents a method to fully characterize the spatio-temporal correlations of PDC entangled photons using sum frequency generation, enabling the reconstruction of their complex X-shaped correlation structure.

Contribution

It introduces a novel scheme combining PDC and sum frequency generation to detect full spatio-temporal correlations of entangled photons, with detailed feasibility analysis.

Findings

The scheme can reconstruct the X-shaped correlation structure.

The method is robust against dispersive elements and misalignments.

Feasibility conditions for experimental implementation are identified.

Abstract

In this work we propose and analyse a scheme where the full spatio-temporal correlation of twin photons/beams generated by parametric down-conversion is detected by using its inverse process, i.e. sum frequency generation. Our main result is that, by imposing independently a temporal delay \Delta t and a transverse spatial shift \Delta x between two twin components of PDC light, the up-converted light intensity provides information on the correlation of the PDC light in the full spatio-temporal domain, and should enable the reconstruction of the peculiar X-shaped structure of the correlation predicted in [gatti2009,caspani2010,brambilla2010]. Through both a semi-analytical and a numerical modeling of the proposed optical system, we analyse the feasibility of the experiment and identify the best conditions to implement it. In particular, the tolerance of the phase-sensitive measurement against the presence of dispersive elements, imperfect imaging conditions and possible misalignments of the two crystals is evaluated.