Quasinormal mode quantization of bound and propagating photons in complex lightguiding nanostructures for integrated devices

TL;DR

This paper develops a comprehensive theoretical framework for quantizing and analyzing quasinormal modes in complex nanostructures used in integrated photonic quantum devices, enabling precise modeling of light-matter interactions.

Contribution

It introduces general boundary conditions and a quantization scheme for interacting quasinormal-mode cavities coupled to quantum emitters and propagating photons, applicable to complex nanostructures.

Findings

Derived boundary conditions for quasinormal modes considering specific geometries.

Presented a general quantization scheme for multiple interacting cavities.

Formulated a system-bath Hamiltonian with computable coupling elements.

Abstract

Open optical or plasmonic resonators are placed on and connected through surfaces or via waveguides, forming complex lightguiding nanostructures, e.g. for integrated photonic quantum devices. We derive general boundary conditions for quasinormal modes that account for the structure's specific geometry. We then present a general quantization scheme for multiple, interacting quasinormal-mode cavities coupled to quantum emitters and to a non-bosonic bath of propagating photons on waveguides or a surface. We derive a system-bath Hamiltonian with rigorously defined coupling elements that can be computed using Maxwell solvers, including light-matter coupling between the electromagnetic field and quantum emitters. We define system-bath correlation functions for an effective, bath-mediated, and time-delayed interaction between the quasinormal modes and quantum emitters, which is a main ingredient commonly used to simulate open quantum system dynamics.