INTERFERENCE, DISTINGUISHABILITY, AND APPARENT CONTRADICTION IN AN EXPERIMENT ON INDUCED COHERENCE

It has been shown in experiments on induced coherence without induced emission using two coherently pumped nonlinear crystals that (a) no second-order interference occurs as long as it is possible, even if only in principle, to determine which of the two crystals emitted the photon pair; (b) second-order interference does occur whenever it is intrinsically impossible to determine which of the two crystals emitted the photon pair. The present paper discusses a variant of the previous experiments in which, apparently, (c) each photon of the pair is emitted by a different crystal. It is also shown that interference is not necessarily reduced when there is no intrinsic indistinguishability. The experiment provides a proof of Bell's theorem for two particles without using an inequality and, at least in principle, could be used to test local realism against quantum mechanics. However, as in the case of the other experiments so far performed, some additional assumption would have to be introduced. It is then shown that the introduction of a reasonable assumption reduces the detectors's efficiencies needed to test local realism, even if nonenhancement is not assumed.