Strongly Entangled System-Reservoir Dynamics With Multiphoton Pulses Beyond The Two-Excitation Limit: Exciting The Atom-Photon Bound State

Within the matrix product state framework, we study the non-Markovian feedback dynamics of a two-level system interacting with the electromagnetic field inside a semi-infinite waveguide where the excitation of an atom-photon bound state is possible. Taking the steady-state excitation of the emitter as a figure of merit, we compare the trapped excitation for an initially excited quantum emitter and an emitter prepared via quantized pulses containing up to four photons. In the latter case, we find that for large feedback delay times, multiphoton pulses can yield a significantly higher steady-state excitation than possible with an initially excited emitter since the stimulated emission process can enhance the trapping probability in comparison to the spontaneous decay of an initially excited emitter.