Emergence of solitons from many-body photon bound states in quantum nonlinear media

Solitons are known to occur in the context of atom-light interaction via well-known semiclassical phenomenon self-induced transparency (SIT). Separately, regime where both light and atoms fully treated quantum mechanically, few-photon bound states be a ubiquitous that arises different systems such as coupled chiral or bidirectional waveguides, Rydberg atomic media. In specific case two-level waveguide, recent analysis based on Bethe ansatz has established SIT emerges from realm superposition many-photon states. Beyond this case, however, nature any connection between full many-body behavior not been established. Here, we employ general spin-model formulation interfaces numerically investigate problem, taking advantage fact approach readily allows for powerful simulations matrix product (MPS). We first analytically derive two-photon state dispersion relation variety then proceed multiexcitation dynamics. Interestingly, all studied, find large-photon number limit always coincides with soliton immediate generalizations thereof.