  Some predictions regarding pre- and post-selected states are far-reaching,
thereby requiring validation with standard quantum measurements in addition to
the customary weak measurements used so far, as well as other advanced
techniques. We go further pursuing this goal, proposing two thought experiments
which incorporate novel yet feasible validation methods of unconventional
light-matter interactions. An excited atom traverses a Mach-Zehnder
interferometer (MZI) under a special combination of pre- and post-selection. In
the first experiment, photons emitted by the superposed atom, after being hit
by two laser beams, are individually counted. Despite the interaction having
definitely taken place, the numbers of photons emitted from each arm of the MZI
are predicted, at the ensemble level, to be different from those expected with
standard stimulated emission. In the second experiment, the atom spontaneously
emits a photon while still in the MZI. This photon later serves as a strong
measurement of the atom's energy upon hitting a photographic plate. The
experiment is repeated to enable an interference effect of the emitted photons.
Interestingly, the latter gives the appearance that the photons have been
emitted by the atom from a position much farther from the two MZI arms L and R,
as if in a "phantom arm" R'. These experiments also emphasize the key role of
anomalous weak values in determining light-matter interactions. In fact, they
present a straightforward realization of an entity we term counter-particles,
namely pre- and post-selected states acting as if they have negative physical
variables such as mass and energy. The novel verification methods we suggest
for testing these predictions resemble weak measurements in some aspects, yet
result from definite atomic transitions verified by the detected photons.
