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.
@article{arxiv.1205.3240,
title = {Phonon number measurements using single photon opto-mechanics},
author = {Sahar Basiri-Esfahani and Uzma Akram and Gerard J. Milburn},
journal= {arXiv preprint arXiv:1205.3240},
year = {2013}
}