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The collective dynamics of two non-interacting two-level emitters, which arecoupled to a structured wave guide that supports two-photon bound states, isinvestigated. Tuning the energy of the two emitters such that they are inresonance with the two-photon bound state energy band, we identify parameterregimes where the system displays fractional populations and essentiallyundamped Rabi oscillations. The Rabi oscillations, which have no analog in thesingle-emitter dynamics, are attributed to the existence of a collectivepolaron-like photonic state that is induced by the emitter-photon coupling. Thefull dynamics is reproduced by a two-state model, in which the photonic polaroninteracts with the state $|e,e,\text{vac} \rangle$ (two emitters in theirexcited state and empty wave guide) through a Rabi coupling frequency thatdepends on the emitter separation. Our work demonstrates that emitter-photoncoupling can lead to an all-to-all momentum space interaction betweentwo-photon bound states and tunable non-Markovian dynamics, opening up a newdirection for emitter arrays coupled to a waveguide.

Undamped Rabi oscillations due to polaron-emitter hybrid states in non-linear photonic wave guide coupled to emitters