Modeling the space-time correlation of pulsed twin beams

TL;DR

This paper introduces a semi-analytic model for describing the space-time correlations of pulsed twin beams generated by parametric down-conversion, bridging the gap between complex simulations and simplified theories.

Contribution

The work presents a new semi-analytic model that accurately predicts quantum correlations and coherence in pulsed twin beams, validated against detailed numerical simulations.

Findings

Correlation size grows as the square root of gain g

Space-time distribution contracts with increasing gain

Model predictions match stochastic numerical simulations

Abstract

Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications, due their multimodal nature in space and time. However, a satisfactory theoretical description is still lacking. In this work we propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory. The model is used to study the quantum correlation and the coherence in the angle-frequency domain of the parametric emission, and demonstrates a $g^{{1/2}} $ growth of their size as the gain $g$ increases, with a corresponding contraction of the space-time distribution. These predictions are systematically compared with the results of stochastic numerical simulations, performed in the Wigner representation, of the full model equations: an excellent agreement is shown even for parameters well outside the expected limit of validity of the model.