  The ability to engineer photon emission and photon scattering is at the heart
of modern photonics applications ranging from light harvesting, through novel
compact light sources, to quantum-information processing based on single
photons. Nanophotonic waveguides are particularly well suited for such
applications since they confine photon propagation to a 1D geometry thereby
increasing the interaction between light and matter. Adding chiral
functionalities to nanophotonic waveguides lead to new opportunities enabling
integrated and robust quantum-photonic devices or the observation of novel
topological photonic states. In a regular waveguide, a quantum emitter radiates
photons in either of two directions, and photon emission and absorption are
reverse processes. This symmetry is violated in nanophotonic structures where a
non-transversal local electric field implies that both photon emission and
scattering may become directional. Here we experimentally demonstrate that the
internal state of a quantum emitter determines the chirality of single-photon
emission in a specially engineered photonic-crystal waveguide. Single-photon
emission into the waveguide with a directionality of more than 90\% is observed
under conditions where practically all emitted photons are coupled to the
waveguide. Such deterministic and highly directional photon emission enables
on-chip optical diodes, circulators operating at the single-photon level, and
deterministic quantum gates. Based on our experimental demonstration, we
propose an experimentally achievable and fully scalable deterministic
photon-photon CNOT gate, which so far has been missing in photonic
quantum-information processing where most gates are probabilistic.
