Controlling two-photon conditional interference

Summary form only given. Greenberger, Horne and Zeilinger have discussed an interesting idealized two-particle double-slit interference experiment. The source is a linear distribution of particles that can decay in two daughter particles. In the decay process, the momenta of the two daughters are approximately equal and opposite. The two double-slits surround the source particle in opposite sides. Tne decay particles can pass either through the slits A and A\´ or B and B\´. The arrival of the particles is registered at the screens. We then measure a product of independent single-particle interference patterns ("independent fringes"). This condition is the requirement to detect the usual Young single-particle interference pattern. Greenberger, Horne and Zeilinger affirm that "there is a sort of complementarity between one- and two-particle fringes: The condition for seeing one-precludes the possibility of seeing the other" We have tested this idealized experiment by using as a source a spontaneous parametric down-converter crystal. A quantum multimode theory was used to calculate the fourth-order correlation function as a function of the detectors positions, for this light source. The above shows that the detection of a fourth-order interference pattern does not guarantee the presence of conditional fringes.