Modeling the space-time correlation of pulsed twin beams

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 g1/2 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.

Automated summary

In this study, a semi-analytic model is proposed to describe the entangled twin beams generated by parametric down-conversion. The model is used to investigate the quantum correlation and coherence of the emitted photons in the angle-frequency domain. The results show that the size of the photons grows with a g1/2 dependence as the gain increases, accompanied by a contraction of the space-time distribution. The predictions of the model are in excellent agreement with stochastic numerical simulations.