Amplification of mechanical quadratures using weak values

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.