High Accuracy, Broadband Simulation of Complex Structures with Quantum Effects, Parallel Fast Algorithm, and Integral Equation Domain Decomposition

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Even though classical electromagnetic theory has been around for over 150 years, its enduring legacy has not diminished. In fact, it finds its way into so many modern day technologies that it is indispensable in the modern world such as in wireless communications, computer technologies, bio-medical engineering, and big data transfer. Two concepts in electromagnetics have emerged in recent past. First is the use of computers and mathematical methods that have appeared in the 20th century to solve highly complex electromagnetics, giving rise to the field of computational electromagnetics (CEM). Second is the study of quantum effects and quantum theory (that also appeared in the 20th century) in electromagnetic systems giving rise to fields like quantum optics that can potentially impact information, communications, and computation technologies such as quantum information, communication, encryption, and computation. This project will combine the use of computational electromagnetics knowledge to understand quantum systems that interact with electromagnetic fields. This will engender the development of future quantum technologies that open new gateways to previously untapped possibilities.This project will develop computational tools to meet the demands of emerging technologies in nano chip, nano optics, and quantum optics. The modeling of electromagnetic and quantum effects in nanostructures has become increasingly important due to the miniaturization of transistors, optical structures, and quantum information systems. But the exorbitant complexity and computational cost of modeling such problems have precluded their precise solution so far. The objective of this proposal is to develop fast computational algorithms that can capture circuit physics, wave physics and quantum effects in order to effectively simulate circuit-quantum electrodynamics (C-QED) systems. This will entail the development of multi-scale, multi-physics solvers while incorporating quantum effects through the use of the dyadic Green?s function. The resulting codes will be validated against experimental results. If successful, this research will open up a new frontier on how C-QED systems can be analyzed using fast, stable and accurate computational algorithms. This in turn would enable new discoveries in C-QED that could impact quantum computing and quantum information processing. Extensive educational outreach activities are planned including the involvement of K-12 and undergraduate students, and the development of visualization tools and video lectures to disseminate results to the public.