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.
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.
Abstract The control of the interaction between quantum emitters using nanophotonic structures holds great promise for quantum technology applications, while its theoretical description for complex nanostructures is a highly demanding task as the electromagnetic (EM) modes form a high‐dimensional continuum. We here introduce an approach that permits a quantized description of the full EM field through a small number of discrete modes. This extends the previous work in ref. (I. Medina, F. J. García‐Vidal, A. I. Fernández‐Domínguez, and J. Feist, “Few‐mode field quantization of arbitrary electromagnetic spectral densities,” Phys. Rev. Lett. , vol. 126, p. 093601, 2021) to the case of an arbitrary number of emitters, without any restrictions on the emitter level structure or dipole operators. The low computational demand of this method makes it suitable for studying dynamics for a wide range of parameters. We illustrate the power of our approach for a system of three emitters placed within a hybrid metallodielectric photonic structure and show that excitation transfer is highly sensitive to the properties of the hybrid photonic–plasmonic modes.
The full information about the interaction between a quantum emitter and an arbitrary electromagnetic environment is encoded in the so-called spectral density. We present an approach for describing such interaction in any coupling regime, providing a Lindblad-like master equation for the emitter dynamics when coupled to a general nanophotonic structure. Our framework is based on the splitting of the spectral density into two terms. On the one hand, a spectral density responsible for the non-Markovian and strong-coupling-based dynamics of the quantum emitter. On the other hand, a residual spectral density including the remaining weak-coupling terms. The former is treated nonperturbatively with a collection of lossy interacting discrete modes whose parameters are determined by a fit to the original spectral density in a frequency region encompassing the quantum emitter transition frequencies. The latter is treated perturbatively under a Markovian approximation. We illustrate the power and validity of our approach through numerical simulations in three different setups, thus offering a variety of scenarios for a full test, including the ultra-strong coupling regime.
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.
Strong coupling of quantum emitters with confined electromagnetic modes of nanophotonic structures may be used to change optical, chemical, and transport properties of materials, with significant theoretical effort invested toward a better understanding of this phenomenon. However, a full theoretical description of both matter and light is an extremely challenging task. Typical theoretical approaches simplify the description of the photonic environment by describing it as a single mode or few modes. While this approximation is accurate in some cases, it breaks down strongly in complex environments, such as within plasmonic nanocavities, and the electromagnetic environment must be fully taken into account. This requires the quantum description of a continuum of bosonic modes, a problem that is computationally hard. We here investigate a compromise where the quantum character of light is taken into account at modest computational cost. To do so, we focus on a quantum emitter that interacts with an arbitrary photonic spectral density and employ the cumulant, or cluster, expansion method to the Heisenberg equations of motion up to first, second, and third order. We benchmark the method by comparing it with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.
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.
While experimental measurements of photon correlations have become routine in laboratories, theoretical access to these quantities for the light generated in complex nanophotonic devices remains a major challenge. Current methods are limited to specific simplified cases and lack generality. Here we present a novel method that provides access to photon statistics resolved in space and frequency in arbitrary electromagnetic environments. Within the macroscopic QED framework, we develop a practical tool to compute electric field correlations for complex quantum systems by including lossy two-level systems that act as field detectors within the system. To make the implementation feasible, we use a recently developed multiemitter few-mode quantization method to correctly account for fully retarded light propagation to the detectors. We demonstrate the effectiveness and robustness of the proposed technique by studying the photon correlations of one and two emitters in close proximity to a plasmonic nanoparticle. The simulations show that even in these relatively simple configurations, the light statistics exhibit a strong angular dependence. These results highlight the importance of going beyond conventional quantum optical approaches to fully capture the analyzed physical effects and enable the study of the quantum light generation in realistic nanophotonic devices.