Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit

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 unitary 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 -π to π, respectively. The results indicate that this hybrid quantum system can act as a quantum router.