Single-photon scattering by a Λ-type three-level in a cavity coupling to one-dimensional waveguide

The scattering of single-photon by a Λ-type three-level embedded in a cavity which is coupled to a one-dimensional waveguide is investigated theoretically by full quantum-mechanical approach. The single-photon transmission amplitude and reflection amplitude are obtained via real-space approach, respectively. It reveals that single-photon can be transmitted or reflected by controlling classic driving field tuning off or on. The effects of dissipations of the cavity and of the atom on the photon transport properties are also discussed.