  We study a tripartite quantum system consisting of a coplanar-waveguide (CPW)
resonator and a nanomechanical resonator (NAMR) connected by a flux qubit,
where the flux qubit has a large detuning from both resonators. By a unitray
transformation and a second-order approximation, we obtain a strong and
controllable (i.e., magnetic-field-dependent) effective coupling between the
NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting
can be observed from the voltage-fluctuation spectrum of the CPW resonator. We
further study the properties of single photon transport as inferred from the
reflectance or equivalently the transmittance. We show that the reflectance and
the corresponding phase shift spectra both exhibit doublet of narrow spectral
features due to vacuum Rabi splitting. By tuning the external magnetic field,
the reflectance and the phase shift can be varied from 0 to 1 and $-\pi$ to
$\pi$, respectively. The results indicate that this hybrid quantum system can
act as a quantum router.
