WAVE CHAOS IN MICROWAVE COUPLED ENCLOSURES, RESERVOIR COMPUTING, AND PHOTONIC TOPOLOGICAL INSULATOR GRAPHS: THEORY AND EXPERIMENT

Complex scattering exists in many diverse physical and real-life scenarios. Examples include reactions of atomic nuclei, transport through quantum dots, and the propagation of electromagnetic (EM) waves in over-moded resonant systems. These systems are Wave Chaotic, meaning that minute perturbations will lead to a drastic change in the wave properties of the system. The underlying chaotic property in the short wavelength limit makes deterministic modeling of wave properties vulnerable to small perturbations. Because of this, statistical methods play a central role in wave chaotic system studies. The Random Coupling Model (RCM) has been successfully applied to predict the statistics of single chaotic EM enclosures. We here expand RCM to systems consisting of multiple volumes that are coupled together, and do so with highly reduced computational complexity. Going beyond knowledge-based modeling, we employ machine-learning techniques to identify hidden information embedded in the scattering properties of wave chaotic systems. Reservoir computing (RC) is a genre of neural networks employed in machine learning studies. Its training is radically simplified (compared to a full back-propagation process in neural networks) because the input and reservoir layers remain unchangedduring the process. Recent work shows that RC can reasonably predict the future evolution of spatio-temporal chaotic systems. We aim to reverse the thinking: to emulate a software RC using the spatio-temporal chaotic wave fields in physical EM enclosures. A proof-of-principle hardware RC is demonstrated experimentally, and tested through a series of complex tasks carried out at ns-time scales. The concept of photonic topological insulator (PTI) is translated from the study of topological insulators (TIs) in condensed matter physics. For a TI material, the charge will only flow in topologically-protected states on the boundary surrounding the material,rather than in the bulk. We experimentally demonstrated a novel composite PTI system with quantum Hall (QH) and quantum spin Hall (QSH) topological phases. The TI effect also introduces a synthetic spin-1/2 degree-of-freedom to the guided waves. The Fermionic two-state property, absent in the bosonic photon world, is now accessible using the PTI system. Using this PTI system, I realize a chaotic graph system that falls in the Gaussian Symplectic Ensemble (GSE) universality class, which in principle only exists in the Fermionic world. We use simulations to show that GSE statistics will emerge in an appropriately designed PTI graph obeying anti-unitary symmetry