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和林德布拉德（特别是描述光传播的系统浴相互作用）奠定理论基础;其主要目标是方法学。由此产生的框架应该使理论和实验物理学家在一定程度上使用现实的（数值）电动力学计算的光子器件超出教科书的例子，以获得哈密顿和Lindbladian的参数。一个重要的重点是在一个可行的方案与快速，定义明确，和可靠的（参数）组之间的交换，一方面侧重于计算光子学和量子光学动力学，另一方面，理解和设计量子器件使用微观计算参数。该项目建立在准简正模（QNM）框架的基础上，该框架为单腔或单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，该模型仅粗略地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。这些方面在量子化中的详细处理和概括-朝向由多个腔、具有束缚模式的等离子体或其他光子结构以及互连（例如，波导）与传播光子-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。以前开发的框架的扩展将允许复杂的空间结构的纳米结构的描述。因此，该项目使用计算光子学技术创建了可行（和快速）参数计算的配方，如在QNM情况下的束缚模式。最后，一组构建块将可用于构建扩展的量子设备或网络的理论描述（算子，哈密顿算子，Lindbladian等），所有这些都是由量子发射器、腔中的束缚模式和类似复杂结构波导的互连所形成的，并且具有用于从计算光子学进行有效耦合元件计算的设定配方。结果允许参数计算，最终可以集成到FEM和FDTD求解器供实验人员使用。该框架的开发包含了对这种扩展量子结构的原型理论应用，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.