  Coherence can be induced or stimulated in parametric down-conversion using
two or three crystals when, for example, the idler modes of the crystals are
aligned. Previous experiments with induced coherence [Phys. Rev. Lett. 114,
053601 (2015)] focused on which-path information and the role of vacuum fields
in realizing complementarity via reduced visibility in single-photon
interference. Here we describe experiments comparing induced and stimulated
coherence. Different single-photon interference experiments were performed by
blocking one of the pump beams in a three-crystal setup. Each counted photon is
emitted from one of two crystals and which-way information may or not be
available, depending on the setup. Distinctly different results are obtained in
the induced and stimulated cases, especially when a variable transmission
filter is inserted between the crystals. A simplified theoretical model
accounts for all the experimental results and is also used to address the
question of whether the phases of the signal and idler fields in parametric
down-conversion are correlated.
