Nonclassicality of induced coherence without induced emission

Interference of two beams produced at separate biphoton sources was first observed more than two decadesago. The phenomenon, often called “induced coherence without induced emission,” has recently gained attentionafter its applications to imaging, spectroscopy, and measuring biphoton correlations have been discovered. Thesources used in the corresponding experiments are nonlinear crystals pumped by laser light. The use of a laserpump makes the occurrence of induced (stimulated) emission unavoidable, and the effect of stimulated emissioncan be observed in the joint detection rate of the two beams. This fact raises the question whether the stimulatedemission also plays a role in inducing the coherence. Here we investigate a case in which the crystals are pumpedwith a single-photon Fock state. We find that coherence is induced even though the possibility of stimulatedemission is now fully ruled out. Furthermore, the joint detection rate of the two beams becomes ideally zero.Our results rule out any classical or semiclassical explanation of the phenomenon and also suggest that it is,in principle, possible to perform similar experiments with fermions, for which stimulated emission is strictlyforbidden.