Polarization Conversion of Single Photon via Scattering by a \Lambda System in a Semi-Infinite Waveguide

We theoretically investigate single-photon polarization conversion via scattering by an atom with \Lambda configuration coupled to a semi-infinite waveguide and discuss the two cases in which the \Lambda system is non-degenerated and degenerated. By applying the hard-wall boundary condition of the semi-infinite waveguide, it is found that single-photon polarization conversion can be realized with unit probability for both cases under the ideal condition. Together with the polarization conversion, the frequency conversion of a single photon can also be realized with unit probability in the ideal case if the \Lambda system is not degenerated.