Recent studies have established and rigorously validated a modified Langevin noise formalism that enables macroscopic-QED-based quantization of electromagnetic fields in open and dissipative environments. Building on this foundation, a multimode Jaynes-Cummings framework has been developed and verified, providing an accurate description of atom-field interactions in lossy and radiative systems. In this work, we explore the potential of this formalism for nanophotonic applications by modeling representative quantum-plasmonic dynamics. In particular, we present detailed numerical examples for (i) two-photon interference mediated by a quantum plasmonic beam splitter, and (ii) non-Markovian dynamics of an atom located in plasmonic antennas and corresponding directional control of out-coupled single-photon fields. These results illustrate how the proposed modeling approach can provide quantitative insight into the behavior of plasmonic single-photon sources and beam-splitting structures.
Recent studies have established and rigorously validated a modified Langevin noise formalism that enables macroscopic-QED-based quantization of electromagnetic fields in open and dissipative environments. Building on this foundation, a multimode Jaynes-Cummings framework has been developed and verified, providing an accurate description of atom-field interactions in lossy and radiative systems. In this work, we explore the potential of this formalism for nanophotonic applications by modeling representative quantum-plasmonic dynamics. In particular, we present detailed numerical examples for (i) two-photon interference mediated by a quantum plasmonic beam splitter, and (ii) non-Markovian dynamics of an atom located in plasmonic antennas and corresponding directional control of out-coupled single-photon fields. These results illustrate how the proposed modeling approach can provide quantitative insight into the behavior of plasmonic single-photon sources and beam-splitting structures.
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.
We present a novel numerical framework that integrates the modified Langevin noise formalism into the multimode Jaynes- and Tavis-Cummings models, enabling a first-principles, non-Markovian analysis of atom-field interactions in dissipative electromagnetic (EM) environments that account for both radiative losses and absorptive dissipation in lossy dielectric media (or satisfying general inhomogeneous causal media exhibiting both dispersion and absorption effects). In the modified Langevin noise formalism, the boundary- and medium-assisted (BA and MA) fields, which constitute a continuum set of EM modes in dissipative EM environments, are numerically obtained using the finite-element method (FEM). Specifically, BA field modes are extracted by solving plane-wave scattering problems, while MA field modes are determined through point-source radiation problems. These numerically obtained BA and MA field modes are then incorporated into the multimode Jaynes- and Tavis-Cummings models such that the coupling strength between atoms and BA-MA field modes can be calculated for the study of atom-field interactions in dissipative EM environments. The proposed methodology captures non-Markovian atomic dynamics that cannot be described by traditional quantum master equations under the Markovian approximation. To validate the accuracy of the proposed numerical framework, we present four numerical examples: (i) a two-level system (TLS) in a perfect electric conductor (PEC) half-space; (ii) dissipative cavity electrodynamics with two limiting cases approaching spontaneous emission in free space and ideal Rabi oscillations; (iii) super-radiance in TLS arrays; and (iv) entanglement sudden death of two TLSs inside dissipative cavities. The proposed methodology can serve as a ground-truth numerical simulator for studying atom-field interactions in general dissipative EM environments.
In this work, we present a numerical framework for modeling single photon emission from a two level system in open and dissipative systems beyond the Markovian approximation. The method can be readily integrated into standard computational electromagnetic (CEM) solvers such as finite difference time domain (FDTD) and finite element method (FEM). We numerically verify the completeness of boundary and medium assisted modes in the modified Langevin noise formalism by reconstructing the imaginary part of the dyadic Greens function through modal expansion in three dimensions. This reconstruction enables a first principles description of atom field interaction via the multi mode Jaynes Cummings model in open and dissipative environments. Within the single excitation manifold, we show that the memory kernel of a two level system is determined by the imaginary part of the Greens function, implying that radiative modes alone govern the relevant dynamics. The proposed framework thus provides a Greens function based approach for describing atomic population and single photon dynamics, directly compatible with Maxwell solvers. We then present concrete strategies for implementing our method in both FDTD and FEM frameworks, demonstrating its practical applicability. We further verify numerical results for a lossy Lorentz Drude type mirror, including both the case of a TLS near a finite sized metallic mirror and that of a TLS centered in a Fabry Perot cavity. This work establishes a rigorous foundation for incorporating quantum emitter dynamics into computational electromagnetics, thereby extending classical solvers toward quantum light matter interactions.
We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral density, obtained through classical electromagnetic simulations, to a model system involving a small number of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and electric field spatial dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.
In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built upon assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.
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.