Spatial distribution of quantum fluctuations in spontaneous down-conversion in realistic situations

Abstract

We show that in the limit of negligible pump depletion, the spatial distribution of the quantum fluctuations in spontaneous parametric down-conversion can be computed for any shape of the pump beam by using the Green's function method to linearize the quantum fluctuations, even for very low levels of the intensities measured on the pixels. The results are in complete agreement with stochastic simulations of the Wigner distribution. Both methods show specific quantum effects in realistic situations close to the experiments now in progress, like sub-shot noise correlation between opposite pixels in the far field.