Non-Markovian analysis of atom-field interactions in dissipative electromagnetic environments

We present a numerical framework that integrates a modified Langevin noise formalism into multimode Jaynes- and Tavis-Cummings models for first-principles, non-Markovian analysis of atom-field interactions in dissipative electromagnetic environments under weak coupling. This formalism enables the quantization of electric field operators in terms of boundary- and medium-assisted modes with real-valued eigenfrequencies, accounting for both radiative and absorptive losses. To efficiently handle the continuum nature of the boundary- and medium-assisted mode spectrum, we apply adaptive frequency refinement and mode-space coarse-graining based on finite-element simulations to obtain a tractable discrete set of field modes. These modes are then used to construct matrix representations of the Schr"odinger equation, enabling direct computation of atomic observables and field quantities---such as single-photon amplitudes and higher-order correlation functions---beyond the Markovian approximation. Importantly, this framework does not rely on any phenomenologically designed memory kernel. Instead, the spectrum of boundary- and medium-assisted modes interacting with atoms inherently and rigorously captures memory effects arising from the open and dissipative electromagnetic environment. We present four numerical examples to validate the proposed framework and demonstrate its ability to model non-Markovian atomic dynamics in open and dissipative electromagnetic environments: (i) a two-level system near the surface of a perfect electric conductor, (ii) dissipative cavity quantum electrodynamics for a single two-level system, (iii) super- and subradiance in two-level system arrays, and (iv) entanglement sudden death between two two-level systems. This framework provides a versatile simulation tool for the design of quantum photonic devices, including nitrogen-vacancy center single-photon sources coupled to plasmonic structures, entangled photon-pair generation near lossy media, and decoherence modeling of solid-state quantum memories based on rare-earth ions and color centers. It is particularly well suited to dissipative quantum electrodynamics in photonic integrated circuits, where accurate modeling of scattering and diffraction is essential.