  Controllable single-photon routing plays an important role in quantum
networks. We investigate single-photon scattering in two one-dimensional (1D)
waveguides by a three-level emitter with a cascade configuration, which is a
dipole coupled to an extra cavity. The tunneling path for the transmission of a
single photon is switched by whether the extra cavity contains photons. For the
setup, the Autler-Townes splitting is modulated by the extra cavity, in which
the transmission valley (reflection range) width is tunable in terms of the
number of photons in the extra cavity. Our investigation will be beneficial to
single-photon routing in quantum networks using quantifiable photon numbers in
an extra cavity.
