Computational framework for non-Markovian multi-emitter dynamics beyond the single-excitation limit

Quantum Physics [Submitted on 3 Apr 2026] Computational framework for non-Markovian multi-emitter dynamics beyond the single-excitation limit Hyunwoo Choi, Weng Cho Chew, Dong-Yeop Na While non-Markovian dynamics have been extensively studied in the single-excitation limit to predict non-trivial phenomena, this regime remains an idealization. Moving beyond it is essential, as optical nonlinearities and phase-error accumulation in multi-photon processes render the Markovian approximation fragile. In this work, 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 (M-LN) formalism is employed for first-principles treatment of dissipative environments, while the emitter-centered mode (ECM) framework ensures computational tractability. Unlike conventional approaches that integrate out the reservoir, we construct a non-Markovian hierarchy of coupled differential equations by explicitly retaining photonic amplitudes. Within the two-excitation hierarchy, the formulation preserves total probability and retains phase information necessary to capture multi-photon interference. As numerical demonstrations, we investigate non-Markovian atom-field interactions in structured semi-infinite waveguide environments. We first consider a homogeneous waveguide as a baseline, observing enhanced Bell-state fidelity in selected configurations. Next, we examine collective decay of symmetric Dicke states in a waveguide with an embedded lossy dielectric slab, revealing selective stabilization and delayed excitation transfer induced by the structured reservoir. Finally, we analyze entanglement dynamics in the same setting, highlighting entanglement sudden birth and oscillatory revivals. In principle, the framework applies to arbitrary electromagnetic environments for which the dyadic Green's function can be obtained numerically, providing a versatile tool for investigating complex non-Markovian multi-photon phenomena beyond the single-excitation limit. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.02741 [quant-ph]   (or arXiv:2604.02741v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.02741 Focus to learn more Submission history From: Dong-Yeop Na Ph.D. [view email] [v1] Fri, 3 Apr 2026 05:23:41 UTC (3,098 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)