  Quantum routing of single photons in a system with two waveguides coupled to
two whispering-gallery resonators (WGRs) are investigated theoretically. With a
real-space full quantum theory, photonic scattering amplitudes along four ports
of the waveguide network are analytically obtained. It is shown that, by
adjusting the geometric and physical parameters of the two-WGR configuration,
the quantum routing properties of single photons along the present waveguide
network can be controlled effectively. For example, the routing capability from
input waveguide to another one can significantly exceed 0.5 near the resonance
point of scattering spectra, which can be achieved with only one resonator. By
properly designing the distance between two WGRs and the waveguide-WGR coupling
strengths, the transfer rate between the waveguides can also reach certain
sufficiently high values even in the non-resonance regime. Moreover, Fano-like
resonances in the scattering spectra are designable. The proposed system may
provide a potential application in controlling single-photon quantum routing as
a novel router.

Quantum Physics