  Photons of a laser beam driving the upper motional sideband of an
optomechanical cavity can decay into photon-phonon pairs by means of an
optomechanical parametric process. The phononic state can subsequently be
mapped to a photonic state by exciting the lower sideband, hence creating
photon-photon pairs out of an optomechanical system. We here demonstrate that
these pairs can violate a Bell inequality when they are measured with photon
counting techniques preceded by small displacement operations in the phase
space. Our results show how to detect non-local light-mechanical correlations
and open the way for device-independent quantum optomechanics where
non-classical light-mechanical correlations can be certified without
assumptions on the state structure or on the measurement devices.
