  The interaction of a propagating pulse of quantum radiation with a localized
quantum system can be described by a cascaded master equation with a distinct
initially populated input and a finally populated output field mode [Phys. Rev.
Lett. 123, 123604 (2019), arXiv:1902.09833v3]. By transformation to an
appropriate interaction picture, we identify the usual Jaynes-Cummings
Hamiltonian between the scatterer and a superposition of the initial and final
mode, with a strength given by the travelling pulse mode amplitude. The
transformation also identifies a coupling of the scatterer with an orthogonal
combination of the two modes. The transformed master equation offers important
insights into the system dynamics and it permits numerically efficient
solutions.
