Theoretical models of hybrid light-matter systems and their applications

Abstract

Controllable light-matter interactions are of central importance to a broad range of problems at the heart of modern theoretical, experimental, and applied physics, particularly in the rapidly expanding areas of nanoscale and quantum science. The past few decades have seen incredible advances in this area, heralding a new era in quantum optics and cavity quantum electrodynamics (QED) characterized by chip-scale, hybrid light-matter platforms with engineered properties. In tandem to providing a rich platform for fundamental study of quantum physics, such systems have been shown to support an incredible variety of applications ranging from quantum communication and quantum information science to biomolecular sensing and cavity-controlled chemistry. This thesis compiles a diverse set of theoretical work involving first-principles mathematical modeling of cavity QED and nanophotonic platforms both for fundamental study and for application. In some cases, a classical description is sufficient. In others, quantum effects are considered. Part I of this dissertation contains introductory material which underpins the published works appearing in Parts II and III. Topics discussed in these four preliminary chapters include a Lagrangian-based approach to modeling light-matter interactions (Chapter 1), oscillator model descriptions of photonic cavities, plasmonic nanoresonators, and quantized light-matter interactions (Chapter 2), theoretical modeling of experimental observables (Chapter 3), and, finally, a survey of phenomena in various parameter regimes realizable in cavity QED and nanophotonic platforms (Chapter 4). Parts II and III enclose six chapters of mostly published work, each focusing on a particular platform realizable in a laboratory setting. Chapters 5 and 6 detail collaborative, joint experimental-theoretical work on hybrid photonic-plasmonic resonators, while Chapter 7 follows with a theoretical analysis of an experimentally probed coupled plasmonic dimer supporting infrared Fano resonances. Chapter 8 extends this work with a theoretical treatment of coupled dielectric cavities, followed by collaborative application to a heterogeneous photonic molecule in Chapter 9. We conclude in Chapter 10 with an in-depth analysis of effective photon-photon interactions in cavity and circuit QED systems, with a particular focus on the realization of quantum many-body phenomena in these platforms. Taken together, the chapters herein comprise a set of varied approaches for theoretically modeling and understanding a diverse range of nanophotonic and cavity QED platforms for the fundamental study, control, and technological application of light-matter interactions.