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

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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.