Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems

TL;DR

This paper introduces a concept linking exceptional points and diabolic points in non-Hermitian systems, showing that the distance between them bounds the system's response strength, with implications for optical and photonic applications.

Contribution

It defines the distance between exceptional and diabolic points and proves its role in limiting the spectral response strength of non-Hermitian systems.

Findings

Small distance implies weak spectral response.

Distance bounds the intensity response to perturbations.

Analysis of optical systems illustrates the theory.

Abstract

Exceptional points are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points, at which only eigenenergies degenerate. Here we connect these two kinds of degeneracies by introducing the concept of the distance of a given exceptional point in matrix space to the set of diabolic points. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this exceptional point. A small distance therefore implies a weak spectral response to perturbations and a weak intensity response to excitations. This finding has profound consequences for physical realizations of exceptional points that rely on perturbing a diabolic point. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. A number of optical and photonics systems are investigated to illustrate the theory.