  We study the dynamics of a single photon pulse travels through a linear
atomic chain coupled to a one-dimensional (1D) single mode photonic waveguide.
We derive a time-dependent dynamical theory for this collective many-body
system which allows us to study the real time evolution of the photon transport
and the atomic excitations. Our analytical result is consistent with previous
numerical calculations when there is only one atom. For an atomic chain, the
collective interaction between the atoms mediated by the waveguide mode can
significantly change the dynamics of the system. The reflectivity of a photon
can be tuned by changing the ratio of coupling strength and the photon
linewidth or by changing the number of atoms in the chain. The reflectivity of
a single photon pulse with finite bandwidth can even approach $100\%$. The
spectrum of the reflected and transmitted photon can also be significantly
different from the single atom case. Many interesting physical phenomena can
occur in this system such as the photonic bandgap effects, quantum entanglement
generation, Fano-like interference, and superradiant effects. For engineering,
this system may serve as a single photon frequency filter, single photon
modulation and may find important applications in quantum information.
