In the Wigner formalism, after giving a general description of a light beam, the theory of parametric down-conversion is developed to second-order in the coupling constant. We then describe the detection process by calculating the auto-correlation and cross-correlations of the signal and idler beams. Four recent experiments are analyzed in detail: interference on a screen, Franson's experiments ͓Phys.
We extend the Wigner function formalism for parametric down-conversion experiments presented in a previous paper ͓Phys. Rev. A 55 3879 ͑1997͔͒ to experiments involving propagation through a dispersive medium ͓Steinberg et al., Phys. Rev. A 45, 6659 ͑1992͔͒, and polarization ͓Kwiat et al., Phys. Rev. A 45, 7729 ͑1992͔͒. ͓S1050-2947͑97͒02009-X͔ PACS number͑s͒: 42.50.Ar, 03.65.Sq, 42.50.Lc
In this article we present a local hidden variables model for all experiments involving photon pairs produced in parametric down conversion, based on the Wigner representation o f the radiation field. A modification o f the standard quantum theory of detection is made in order to give a local realistic explanation o f the counting rates in photodetectors. This model involves the existence of a real zeropoint field, such that the vacumm level of radiation lies below the threshold of the detectors.
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