  A model for a controlled single-photon beam-splitter is proposed and
analysed. It consists of two crossed optical-cavities with overlapping waists,
dynamically coupled to a single flying atom. The system is shown to route a
single photon with near-unity efficiency in an effective "weak-coupling"
regime. Furthermore, two such nodes, forming a segment of a quantum network,
are shown to perform several controlled quantum operations. All one-qubit
operations involve a transfer of a photon from one cavity to another in a
single node, while two-qubit operations involve transfer from one node to a
next one, coupled via an optical fiber. Novel timing protocols for classical
optical fields are found to simplify possible experimental realizations along
with achievable effective parameter regime. Though our analysis here is
restricted to a cavity-QED scenario, basic features of the model can be
extended to various other physical systems including gated quantum dots,
circuit-QED or opto-mechanical elements.
