  In a recent paper [I.I. Arkhipov, Phys. Rev. A 98, 021803 (2018)], it was
shown that one can completely identify the nonclassicality of single- and
two-mode Gaussian states by means of certain nonclassicality witnesses which
are based on intensity moments up to the third order of optical fields,
provided that an appropriate coherent displacement is applied to a given
Gaussian state. Here, we utilize a mathematical equivalence between the
description of the coherent displaced Gaussian states generated in the
spontaneous parametric processes and the Gaussian states generated in the
corresponding stimulated parametric processes. Resorting to that equivalence,
we study and compare the power of those nonclassicality witnesses in the
detection of the nonclassicality of the two-mode Gaussian states generated in
both the spontaneous and stimulated second subharmonic and down-conversion
processes and which are subsequently subject to a beam splitter. We demonstrate
that by means of an appropriate induced stimulated emission one can completely
identify the nonclassicality of the considered Gaussian states in comparison to
the case of the spontaneous emission. This is important from the experimental
point of view, as the stimulated emission can be easily implemented in running
optical experiments, and such method can exploit just simple linear detectors.
