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.

中文翻译：

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累积膨胀，用于处理任意材料结构中的光-物质相互作用。

量子发射器与纳米光子结构的受限电磁模式的强耦合可以用于改变材料的光学，化学和传输性质，并投入大量的理论努力来更好地理解这种现象。然而，对物质和光的完整理论描述是一项极富挑战性的任务。典型的理论方法通过将光子环境描述为单个模式或几个模式来简化对光子环境的描述。尽管此近似值在某些情况下是准确的，但在复杂的环境中（例如在等离子纳米腔内）会严重崩溃，必须充分考虑电磁环境。这需要对连续波子模式的量子描述，这是一个计算难题。我们在这里研究一种折衷方案，其中以适度的计算成本考虑了光的量子特性。为此，我们将重点放在与任意光子光谱密度相互作用的量子发射器上，并将累积量或簇扩展方法应用于直到一阶，二阶和三阶的海森堡运动方程。通过将其与特定情况下的精确解决方案进行比较，我们对该方法进行了基准测试，结果表明该方法可以准确表示许多参数范围内的动力学。