Few- and many-body photon bound states in quantum nonlinear media: a spin-model approach
Giuseppe Calajò, Darrick E. Chang · arXiv (Cornell University) · 2021
The emergence of multi-photon bound states in quantum nonlinear media is an intriguing phenomenon that has attracted significant theoretical and experimental interest. Such bound states can emerge in quite different settings, such as arrays of quantum emitters coupled to photonic waveguides and Rydberg nonlinear media. The theoretical tools to characterize the bound states are equally diverse, ranging from Bethe ansatz to effective field theories. Here, we propose and utilize a spin-model formulation of quantum atom-light interactions as a general, unified framework to study bound states, and apply this formalism to several distinct systems. We show how to obtain the bound-state dispersion relation within the two-excitation subspace, and also numerically investigate how the properties of higher multi-photon bound states manifest themselves in the propagation of large photon number pulses and spatio-temporal correlations at the output. Interestingly, for all the specific systems studied (chiral and bi-directional waveguides, and Rydberg media), we find that the large-photon number limit always coincides with the well-known semi-classical soliton phenomenon of self-induced transparency or immediate generalizations thereof.