  We study the controllable single-photon scattering via a one-dimensional
waveguide which is coupled to a two-level emitter and a single-mode cavity
simultaneously. The emitter and the cavity are also coupled to each other and
form a three-level system with cyclic transitions within the zero- and
single-excitation subspaces. As a result, the phase of emitter-cavity coupling
strength serves as a sensitive control parameter. When the emitter and cavity
locate at the same point of the waveguide, we demonstrate the Rabi splitting
and quasidark-state--induced perfect transmission for the incident photons.
More interestingly, when they locate at different points of the waveguide, a
controllable nonreciprocal transmission can be realized and the non-reciprocity
is robust to the weak coupling between the system and environment. Furthermore,
we demonstrate that our theoretical model is experimentally feasible with
currently available technologies.
