  An interferometric arrangement is proposed in which the technique of weak
value amplification is implemented in order to enlarge the effect of a single
photon on the quadratures of a movable mirror of an optical cavity. The photon
interacts weakly with the mirror via radiation pressure and is post-selected in
the dark port of the interferometer. The real and imaginary parts of weak
values of angular momentum type photonic operators produce an amplification of
the mirror quadratures, which is large as compared to the scenario in which all
photons are taken into consideration, i.e. when no post-selection is performed.
The effect is studied both for a mirror initialized in a thermal and coherent
states. For a thermal state, the weak value amplification effect is boosted
with the number of particles of the mirror, which occurs due to the imaginary
part of the weak values.
