The interference of signal and idler waves produced by optical parametric down-conversion was the object of a classic paper by Ghosh and Mandel [Phys. Rev. Lett. 1987, 59, 1903–1905] many years ago. In this paper we investigate the problem in the continuous variable regime, with the aim of identifying quantum signatures that arise from the entanglement of signal and idler waves. By using a model which allows for analytical calculations we show first of all that no quantum features appear for the interference in the fourth-order correlation function in the high-gain regime of parametric down-conversion. The quantum signatures emerge instead from the spatio-temporal correlation function of a generic quadrature component, and we demonstrate that they are clearly linked to the signal/idler entanglement. Relevant and useful links with the theory of quantum images complete the picture.
Lugiato, L. A., Gatti, A., Brambilla, E., & Caspani, L. (2010). Quantum signatures in the interference of macroscopic signal-idler beams. Journal of Modern Optics, 57(14-15), 1273-1280. https://doi.org/10.1080/09500340903576441