Distinct single photons strongly interacting at a single atom in a waveguide

We propose a waveguide QED system where two distinct single photons can interact strongly. The system consists of a single ladder-type three level atom coupled to a waveguide. We show that the nonlinear interaction can be tremendously enhanced by the strong coupling of the cascade atomic transitions to the waveguide mode simultaneously. As a result, a control photon tuned to the upper transition induces a $\pi$ phase shift and tunneling of a probe photon tuned to the otherwise reflective lower transition. Waveguide QED schemes could be an alternative to high quality cavities or dense atomic ensembles in quantum information processing.