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