We investigate the open dynamics of a qubit due to scattering of a single
photon in an infinite or semi-infinite waveguide. Through an exact solution of
the time-dependent multi-photon scattering problem, we find the qubit's
dynamical map. Tools of open quantum systems theory allow us then to discuss
the general features of this map, find the corresponding non-Linbladian master
equation, and assess in a rigorous way its non-Markovian nature. The qubit
dynamics has distinctive features that, in particular, do not occur in emission
processes. Two fundamental sources of non-Markovianity are present: the finite
width of the photon wavepacket and the time delay for propagation between the
qubit and the end of the semi-infinite waveguide.Comment: Integrated the supplementary material into main text and added the
discussion on P-/CP-divisibility. To appear in New Journal of Physic
