Eur. Phys. J. D 29, 437-444 (2004)
https://doi.org/10.1140/epjd/e2004-00040-4

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

Comparison between the stochastic approach and the Green's function method

¹ Laboratoire d'Optique P.M. Duffieux, Institut Femto ST, UMR 6174 du CNRS, Université de Franche-Comté, 25030 Besançon Cedex, France
² Laboratoire Kastler Brossel, UMR 8552 du CNRS, Université Pierre et Marie Curie, case 74, 75252 Paris Cedex 05, France
³ INFM, Dipartimento di Scienze CC.FF.MM., Universitá dell'Insubria, Via Valleggio 11, 22100 Como, Italy

Corresponding author: ^a elantz@univ-fcomte.fr

Received: 2 October 2003
Revised: 15 January 2004
Published online: 23 March 2004

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.