  We describe a system composed of two coupled optical cavity modes with a
coupling modulated by a bulk mechanical resonator. In addition, one of the
cavity modes is irreversibly coupled to a single photon source. Our scheme is
an opto-mechanical realisation of the Jaynes-Cummings model where the qubit is
a dual rail optical qubit while the bosonic degree of freedom is a matter
degree of freedom realised as the bulk mechanical excitation. We show the
possibility of engineering phonon number states of the mechanical oscillator in
such a system by computing the conditional state of the mechanics after
successive photon counting measurements.
