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.
