  Tailored photonic cavities allow enhancing light-matter interaction
ultimately to create a fully coherent quantum interface. Here, we report on an
integrated microdisk cavity containing self-assembled quantum dots to
coherently route photons between different access waveguides. We measure a
Purcell factor of $F_{exp}=6.9\pm0.9$ for a cavity quality factor of about
10,000, allowing us to observe clear signatures of coherent scattering of
photons by the quantum dots. We show how this integrated system can coherently
re-route photons between the drop and bus ports, and how this routing is
controlled by detuning the quantum dot and resonator, or through the strength
of the excitation beam, where a critical photon number less than one photon per
lifetime is required. We discuss the strengths and limitations of this
approach, focusing on how the coherent scattering and single-photon
nonlinearity can be used to increase the efficiency of quantum devices such as
routers or Bell-state analyzers.
