  In quantum communication and distributed quantum computing, one-dimensional
waveguides provide directional transfer of quantum information. A single-mode
waveguide has a density-of-states singularity at the lower cut-off frequency,
which resembles sharp resonances of a cavity but with non-Markovian dynamics.
Thus we put forward schemes of coupling atomic transitions and a waveguide
continuum edge. We first present a scheme of spin-photon quantum interface
operating in the non-Markovian regime for a $\Lambda$-type three-level system
coupled to a waveguide. Then we show that strong coupling between atomic
transitions and a waveguide continuum edge can lead to vacuum Rabi oscillations
and bound polariton states.
