Atom-Field Non-Markovian Dynamics in Open and Dissipative Systems: An Efficient Memory-Kernel Approach Linked to Dyadic Greens Function and CEM Treatments

TL;DR

The paper develops a first-principles framework to model non-Markovian atom–field dynamics of a two-level system in open, lossy environments by marrying the modified Langevin-noise formalism with boundary- and medium-assisted BA–MA modes. It proves that the memory kernel governing atomic population dynamics is tied to the imaginary part of the dyadic Green’s function, enabling a Green’s-function–based description compatible with Maxwell solvers. The authors provide practical FEM and FDTD implementations, verify BA–MA completeness in 3D, and demonstrate non-Markovian emission and Purcell-control effects in lossy mirrors and Fabry–Perot cavities. This work extends computational electromagnetics into the quantum regime, offering a scalable route to simulate quantum emitters in realistic nanophotonic structures. The framework paves the way for optimized single-photon sources and integrated quantum photonic devices under non-Markovian conditions.

Abstract

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.

Figures (14)

• Figure 1: Fluctuations based on the fluctuation--dissipation theorem: (a) radiation-induced loss and corresponding field fluctuation, and (b) medium-induced loss and associated material fluctuation.
• Figure 2: Schematic of the total-field/scattered-field (TFSF) formulation, where only the scattered field exists at the atom position.
• Figure 3: Representative 3D configurations used to verify the completeness of BA–MA modes: (a) a lossy dielectric sphere in free space, and (b) a lossy dielectric sphere inside a PEC cavity.
• Figure 4: Material properties of the dielectric sphere.
• Figure 5: Numerical verification of the BA--MA mode completeness: (a) a lossy dielectric in free space and (b) inside a PEC cavity.