Photon--photon interactions with inner coupled double-cavity

This paper describes the interaction between two spatial modes of the optical fields with a single atom trapped inner coupled double-cavity. Theoretical derivation and numerical simulation with the experimental available parameters show that photon--photon switching and \pi phase shift of single photons may be achieved with current experimental technology. As the probe and control fields are in different spatial modes, the system is superior for implementing cavity QED-based photonic quantum networks.