Connecting classical electrodynamics and quantum dynamics – a framework for quantizing photons in spatially extended quantum nanodevices

该项目将为建立哈密顿量和林德布拉迪亚量（特别是描述光传播的系统浴相互作用）建立理论基础；其主要目标是方法论。由此产生的框架应该使理论物理学家和某种程度上的实验物理学家能够使用现实的（数值的）光子器件的电动力学计算，而不是教科书上的例子来获得哈密顿和林德布拉迪亚的参数。一个重要的重点是一个可行的方案，在组之间快速，定义良好，可靠的（参数）交换，一方面关注计算光子学，另一方面关注量子光学动力学，利用微观计算参数来理解和设计量子器件。该项目建立在准正模（QNM）框架的基础上，该框架为单个腔或单个等离子体结构的广义Jaynes-Cummings模型提供了一个可靠的方案，几乎没有贡献QNM。然而，该模型仅初步涵盖了输入和输出关系，探测器理论以及通过系统浴相互作用在腔外传播的方面。在量子化中对这些方面进行详细的处理和推广-面向由多个腔，等离子体或其他具有束缚模式的光子结构组成的扩展量子器件和网络，以及具有传播光子的互连（例如波导）-是该项目的主要目标，重点是奠定理论基础。这些结构的应用范围从单光子和纠缠光等量子光到量子通信、量子密码学、量子门和寄存器。先前开发的框架的扩展将允许描述复杂的空间结构纳米结构。因此，该项目创建了一个可行的（和快速的）参数计算方法，使用计算光子学技术，如QNM情况下的束缚模式。最后，一组构建模块将可用于构建扩展的量子设备或网络的理论描述（算子，哈密顿，林德布拉迪亚等），所有这些都来自量子发射器，腔中的束缚模式，以及像复杂结构波导一样的互连，以及来自计算光子学的有效耦合元件计算的一组配方。该结果允许参数计算，最终可以集成到FEM和FDTD求解器中，供实验人员使用。该框架的发展包含了一个原型理论应用于这种扩展的量子结构，以测试和证明其可行性。

The project will develop a theoretical foundation for building Hamiltonians and Lindbladians (particularly system-bath interactions for describing light propagation); its main objective is methodological. The resulting framework should enable theoretical and to some extent experimental physicists to use realistic (numerical) electrodynamic calculations of photonic devices beyond textbook examples to get Hamiltonians’ and Lindbladians’ parameters. A significant emphasis is on a feasible scheme with a fast, well-defined, and reliable (parameter) exchange between groups, focusing on computational photonics on the one hand and quantum optical dynamics, on the other hand, to understand and design quantum devices using microscopic calculated parameters. The project builds upon the quasi-normal mode (QNM) framework, which provides a reliable scheme for a generalized Jaynes-Cummings model for a single cavity or a single plasmonic structure with few contributing QNM. However, the model only rudimentarily covers the aspects of input- and output relations, detector theory, and propagation outside of the cavity via system-bath interaction. A detailed treatment and generalization of these aspects in the quantization - towards extended quantum devices and networks consisting of multiple cavities, plasmonic or other photonic structures with bound modes, and interconnects (e.g., waveguides) with propagating photons - is the primary objective of the project with emphasis on laying the theoretical foundation. The applications of these structures range from quantum light such as single photons and entangled light to quantum communication, quantum cryptography, quantum gates, and registers. The extension of the previously developed framework will allow a description of complex spatially structured nanostructures. Therefore, the project creates recipes for a feasible (and fast) parameter calculation using computational photonics techniques like in the QNM case for the bound modes. In the end, a set of building blocks will be available to build an extended quantum device’s or network’s theoretical description (operators, Hamiltonians, Lindbladian, etc.), all buildup from quantum emitters, bound modes in cavities, and interconnects like complex structured waveguides, and with set recipes for efficient coupling element calculations from computational photonics. The outcome allows parameter calculation that can eventually be integrated into FEM and FDTD solvers for usage by experimentalists. The development of the framework contains a prototypical theoretical application to such extended quantum structures to test and prove its feasibility.