Non-reciprocal transmission and non-hermitian quantum sensing using defective operators

Abstract

Operators play a crucial role in the field of physics, especially in quantum mechanics and optics, serving as mathematical tools for describing transformations and physical quantities. While normal operators (i.e., Hermitian and unitary operators) have received significant attention, less is known about non-normal operators that may emerge in various physical systems and effects. Defective operators are a particular type of non-normal operator char acterized by their non-diagonalizability. Recently, research has revealed the occurrence of defective operators in systems with complete non-reciprocity of light and degeneracy of eigen values and eigenvectors of Hamiltonian. These systems have important applications, such as the isolation of light and quantum sensing. This thesis aims to investigate the physics and applications of systems where defective operators arise.