2-SLIT EXPERIMENT WITH DOWNCONVERTED BEAMS

An interesting experiment has been performed by Ribeiro et al. (Phys. Rev. A 49 (1994) 4176) using downconverted beams in a two-slit arrange ment. In this experiment a degree of visibility of Young's fringes beh ind two-slit screen in signal beam can be controlled by change of widt h of pinhole in the idler beam, when coincidence measurement scheme is applied. In this communication the experiment is described using the fourth-order quantum correlation function. Assuming that frequency and phase matching conditions are exactly fulfilled, the calculation of t he coincidence rate leads to a similar result as can be obtained with the help of the fourth order Van Cittert-Zernike theorem expressed in the Fraunhofer approximation. However, the entanglement of downconvert ed beams is effectively equivalent to a change of the ''effective'' so urce area contributing to the Van Cittert-Zemike integral caused by th e change of diameter of the idler pinhole. Thus for sufficiently small idler pinhole the fourth-order interference appears regardless of the fact that linear dimensions of the second-order coherence area are sm aller than the distance between slits.