  We analyze theoretically how to use the radiation pressure coupling between a
mechanical oscillator and an optical cavity field to generate in a heralded way
a single quantum of mechanical motion (a Fock state), and release on-demand the
stored excitation as a single photon. Starting with the oscillator close to its
ground state, a laser pumping the upper motional sideband leads to dynamical
backaction amplification and to the creation of correlated photon-phonon pairs.
The detection of one Stokes photon thus projects the macroscopic oscillator
into a single-phonon Fock state. The non-classical nature of this mechanical
state can be demonstrated by applying a readout laser on the lower sideband
(i.e. optical cooling) to map the phononic state to a photonic mode, and by
performing an autocorrelation measurement on the anti-Stokes photons. We
discuss the relevance of our proposal for the future of cavity optomechanics as
an enabling quantum technology.
