  Light-matter interactions that are nonlinear with respect to the photon
number reveal the true quantum nature of coherent states. We characterize how
coherent states depart from Gaussian by the emergence of negative values in
their Wigner function during the evolution while maintaining their
characteristic Poissonian photon statistics. Such states have non-minimum
uncertainty yet present a metrological advantage that can reach the Heisenberg
limit. Non-Gaussianity of light arises as a general property of nonlinear
interactions, which only requires a polarizable media, resonant or dispersive.
Our results highlight how useful quantum features can be extracted from the
seemingly most classical states of light, a relevant phenomenon for quantum
optics applications.
