Disclosing phonon squeezing by non-equilibrium optical experiments

Fluctuations of the atomic positions are at the core of a large class of unusual material properties ranging from quantum para-electricity and charge density wave to, possibly, high temperature superconductivity. Their measurement in solids is subject of an intense scientific debate focused on the research of a methodology capable of establishing a direct link between the variance of the ionic displacements and experimentally measurable observables. Here we address this issue by means of non-equilibrium optical experiments performed in shot-noise limited regime. The variance of the time dependent atomic positions and momenta is directly mapped into the quantum fluctuations of the photon number of the scattered probing light. A fully quantum description of the non-linear interactions between photonic and phononic fields unveils evidences of squeezing of thermal phonons in $\alpha-$quartz.