Remote macroscopic entanglement on a photonic crystal architecture

The outstanding progress in nanostructure fabrication and cooling technologies allows what was unthinkable a few decades ago: bringing single-mode mechanical vibrations to the quantum regime. The coupling between photon and phonon excitations is a natural source of nonclassical states of light and mechanical vibrations, and its study within the field of cavity optomechanics is developing lightning fast. Photonic crystal cavities are highly integrable architectures that have demonstrated the strongest optomechanical coupling to date and should therefore play a central role for such hybrid quantum-state engineering. In this context, we propose a realistic heralding protocol for the on-chip preparation of remotely entangled mechanical states, relying on the state-of-the-art optomechanical parameters of a silicon-based nanobeam structure. Pulsed sideband excitation of a Stokes process, combined with single-photon detection, allows the writing of a delocalized mechanical Bell state in the system, signatures of which can then be read out in the optical field. A measure of entanglement in this protocol is provided by the visibility of a characteristic quantum interference pattern in the emitted light.