Nonclassical Correlations between Photons and Phonons of Center-of-Mass Motion of a Mechanical Oscillator

We demonstrate nonclassical correlations between phonons and photons created using opto-mechanical spontaneous parametric down-conversion in a system based on a soft-clamped ultracoherent membrane oscillator inside of a Fabry-Pérot optical resonator. Non-Gaussian quantum features are demonstrated for the center-of-mass motion of a submillimeter nanogram-scale mechanical oscillator. We show that phonons stored in the mechanical oscillator, when subsequently read out, display strong signs of quantum coherence, which we demonstrate by single-photon counting enabled by our state-of-the-art optical filtering system. We observe a violation of the classical two-time Cauchy-Schwarz inequality between a heralding write photon and a stored phonon with a confidence of >92%.