Interference of two beams produced at separate biphoton sources was first
observed more than two decades ago. The phenomenon, often called "induced
coherence without induced emission", has recently gained attention after its
applications to imaging, spectroscopy, and measuring biphoton correlations have
been discovered. The sources used in the corresponding experiments are
nonlinear crystals pumped by laser light. The use of a laser pump makes the
occurrence of induced (stimulated) emission unavoidable and the effect of
stimulated emission can be observed in the joint detection rate of the two
beams. This fact raises the question whether the stimulated emission also lays
a role in inducing the coherence. Here we investigate a case in which the
crystals are pumped with a single-photon Fock state. We find that coherence is
induced even though the possibility of stimulated emission is now fully ruled
out. Furthermore, the joint detection rate of the two beams becomes ideally
zero and does no longer change with the pump power. We illustrate our results
by numerical simulations and by comparisons with experimental findings. Our
results rule out any classical or semi-classical explanation of the phenomenon
and also imply that similar experiments can be performed with fermions, for
which stimulated emission is strictly forbidden.Comment: 8 pages, 3 figure
