Two emitters coupled to a bath with Kerr-like nonlinearity: Exponential decay, fractional populations, and Rabi oscillations

We consider two noninteracting two-level emitters that are coupled weakly to a one-dimensional nonlinear waveguide. Due the Kerr-like nonlinearity, waveguide considered supports---in addition scattering continuum---a two-body bound state. As such, models bath with nontrivial mode structure. Solving time-dependent Schr\"odinger equation, radiation dynamics of emitters, initially prepared in their excited states, is presented. Changing emitter frequency such two-emitter energy resonance one ranging from exponential decay fractional populations Rabi oscillations observed. Along detuning, dependence on separation investigated. Approximate reduced Hilbert-space formulations, which result effective and momentum dependent interactions, elucidate underlying physical mechanisms provide an avenue showcase features would be absent if did not contain nonlinearity. Our theoretical findings apply number experimental platforms predictions can tested state-of-the-art technology. In addition, weak-coupling equation based results critical guidance for development master approaches.