  Optical emitters strongly coupled to photons propagating in one-dimensional
waveguides are a promising platform for optical quantum information processing.
Here, we present a theoretical study of the scattering of two indistinguishable
photons on a single two-level atom in a Hong-Ou-Mandel set-up. By computing the
dynamics, we can describe the system at any time of the scattering event. This
allows us to highlight the one-to-one correspondence between the saturation of
the atom and the effective interaction induced between the photons.
Furthermore, we discuss the integrability of the atomic beamsplitter and
provide an intuitive picture for the correlations observed between the outgoing
photons.
