Jaynes-Cummings interaction with a traveling light pulse

The Jaynes-Cummings model provides a simple and accurate description of the interaction between a two-level quantum emitter and a single mode of quantum radiation. Due to the multimode continuum of eigenmodes in free space and in waveguides, the Jaynes-Cummings model should not be expected to properly describe the interaction between an emitter and a traveling pulse of quantum radiation. In this article, we review a cascaded quantum system approach that accurately describes the interaction of a quantum system with an incident quantum pulse of radiation. When applied to the two-level system, different iterations of this approach lead to master equations with different Jaynes-Cummings-like Hamiltonians and damping terms.