Nonlinear Quantum Optics in a Waveguide: Distinct Single Photons Strongly Interacting at the Single Atom Level

We propose a waveguide-QED system where two single photons of distinct frequency or polarization interact strongly. The system consists of a single ladder-type three level atom coupled to a waveguide. When both optical transitions are coupled strongly to the waveguide's mode, we show that a control photon tuned to the upper transition induces a π phase shift and tunneling of a probe photon tuned to the otherwise reflective lower transition. Furthermore, the system exhibits single photon scattering by a classical control beam. Waveguide-QED schemes could be an alternative to high quality cavities or dense atomic ensembles in quantum information processing.