Computational framework for non-Markovian multiemitter dynamics beyond the single-excitation limit
Phys. Rev. A 114, 043733 – Published 21 October, 2026
DOI: https://doi.org/10.1103/k7pc-tc93
Abstract
While non-Markovian quantum electrodynamics has been extensively studied in the single-excitation limit, this restriction excludes the minimal nonlinear sector required to describe saturation, cascaded emission, two-photon correlations, and reservoir-mediated entanglement. In this article, we present a Green's-function-based framework for modeling non-Markovian multi-emitter quantum electrodynamics within the two-excitation manifold. The modified Langevin noise formalism quantizes the coupled electromagnetic-reservoir polaritonic field, incorporating radiative leakage and material absorption at the Hamiltonian level, while the emitter-centered mode transformation reduces the emitter-accessible continuum to a minimal set of collective bright modes. The relevant reservoir amplitudes can therefore be propagated explicitly without tracing out the environment. Within this representation, we propagate the atomic amplitudes together with the intermediate one-environmental-excitation and pure two-environmental-excitation amplitudes. The resulting closed hierarchy retains the full frequency dependence of the environment, capturing spectral memory, retardation, and collective interference while providing access to atomic populations, entanglement, and emitted-field intensity. We demonstrate the framework using analytically modeled semi-infinite one-dimensional environments and a full-wave two-dimensional structure. The one-dimensional examples exhibit collective emission control, delayed excitation transfer, and redistribution between Dicke channels. We then import finite-element Green's-function data for coupled lossy ring resonators. The same hierarchy captures entanglement sudden birth from an initially separable state and reconstructs the associated spatial field distribution. Comparison with an on-shell Markovian reference shows how the full electromagnetic spectrum modifies the onset and persistence of entanglement. The framework thus directly connects electromagnetic Green's functions with correlated atom-field dynamics beyond the single-excitation limit.
