  Interfacing a single photon with another quantum system is a key capability
in modern quantum information science. It allows quantum states of matter, such
as spin states of atoms, atomic ensembles or solids, to be prepared and
manipulated by photon counting and, in particular, to be distributed over long
distances. Such light-matter interfaces have become crucial to fundamental
tests of quantum physics and realizations of quantum networks. Here we report
non-classical correlations between single photons and phonons -- the quanta of
mechanical motion -- from a nanomechanical resonator. We implement a full
quantum protocol involving initialization of the resonator in its quantum
ground state of motion and subsequent generation and read-out of correlated
photonphonon pairs. The observed violation of a Cauchy-Schwarz inequality is
clear evidence for the non-classical nature of the mechanical state generated.
Our results demonstrate the availability of on-chip solid-state mechanical
resonators as light-matter quantum interfaces. The performance we achieved will
enable studies of macroscopic quantum phenomena as well as applications in
quantum communication, as quantum memories and as quantum transducers.
