  We bring together a cavity-enhanced light-matter interface with a multimode
interferometer (MMI) integrated onto a photonic chip and demonstrate the
potential of such hybrid systems to tailor distributed entanglement in a
quantum network. The MMI is operated with pairs of narrowband photons produced
a priori deterministically from a single 87Rb atom strongly coupled to a
high-finesse optical cavity. Non-classical coincidences between photon
detection events show no loss of coherence when interfering pairs of these
photons through the MMI in comparison to the two-photon visibility directly
measured using Hong-Ou-Mandel interference on a beam splitter. This
demonstrates the ability of integrated multimode circuits to mediate the
entanglement of remote stationary nodes in a quantum network interlinked by
photonic qubits.
