Many-photon Scattering and Entangling in a Waveguide with a A-type Atom

We develop the analytical theory that describes simultaneous transmission of several photons through a waveguide coupled to a A-type atom. We show that after transmission of a short few-photon pulse, the final state of the atom and all the photons is a genuine multipartite entangled state belonging to the W class. The parameters of the input pulse are optimized to maximize the efficiency of three- and four-partite W-state production. The probability to obtain the canonical W state of many photons is shown to be larger than 1/e.