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 towards 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 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 with exact solutions for specific situations and show that it can accurately represent dynamics for many parameter ranges.Light-matter interaction is of paramount importance for unraveling the laws of nature and its deep understanding allows us to control and manipulate physical and chemical systems. In particular, one can modify the properties of a quantum emitter simply by changing its electromagnetic environment, for example by enclosing it within an optical cavity. This may give rise to a change of the decay rate for spontaneous emission in the weak coupling regime, the so-called Purcell effect 1 , or to the appearance of hybrid light-matter states, socalled polaritons, in the strong-coupling regime 2-5 . Over the last decades, it has been shown that strong light-matter coupling can be achieved using a large variety of physical implementations as the "cavity" that provides the electromagnetic field confinement. These include Fabry-Perot cavities consisting of two mirrors 5 , propagating surface plasmon polaritons 6 , plasmonic hole 7 and nanoparticle arrays 8 , isolated plasmonic nanoparticles 9 and nanoparticle-on-mirror geometries 10,11 , as well as hybrid cavities combining plasmonic and dielectric materials [12][13][14] . In many of these systems, the electromagnetic field modes are not well-described by isolated lossy cavity modes, and a correct treatment demands theoretical approaches that are able to deal with the complexity of the electromagnetic field modes and their spectrum.In principle, to treat the problem of light-matter interaction, one can rely on the most general theory that describes light and matter on equal footing, i.e., quantum electrodynamics (QED) 15 . However, treating all light and matter degrees of freedom in the systems described above in a quantum mechanical way is an intractable problem and approx...

In the past decade, much theoretical research has focused on studying the strong coupling between organic molecules (or quantum emitters, in general) and light modes. The description and prediction of polaritonic phenomena emerging in this light−matter interaction regime have proven to be difficult tasks. The challenge originates from the enormous number of degrees of freedom that need to be taken into account, both in the organic molecules and in their photonic environment. On one hand, the accurate treatment of the vibrational spectrum of the former is key, and simplified quantum models are not valid in many cases. On the other hand, most photonic setups have complex geometric and material characteristics, with the result that photon fields corresponding to more than just a single electromagnetic mode contribute to the light−matter interaction in these platforms. Moreover, loss and dissipation, in the form of absorption or radiation, must also be included in the theoretical description of polaritons. Here, we review and offer our own perspective on some of the work recently done in the modeling of interacting molecular and optical states with increasing complexity.

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

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.