  We theoretically investigate the quantum scattering of a single-photon pulse
interacting with an ensemble of $\Lambda$-type three-level atoms coupled to a
one-dimensional waveguide. With an effective non-Hermitian Hamiltonian, we
study the collective interaction between the atoms mediated by the waveguide
mode. In our scheme, the atoms are randomly placed in the lattice along the
axis of the one-dimensional waveguide, which closely corresponds to the
practical condition that the atomic positions can not be controlled precisely
in experiment. Many interesting optical properties occur in our waveguide-atom
system, such as electromagnetically induced transparency (EIT) and optical
depth. Moreover, we observe that strong photon-photon correlation with quantum
beats can be generated in the off-resonant case, which provides an effective
candidate for producing non-classical light in experiment. With remarkable
progress in waveguide-emitter system, our scheme may be feasible in the near
future.
