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

Abstract

Exceptional points (EPs) 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 (DPs), at which only eigenenergies degenerate. Here, we connect these two kinds of degeneracies by introducing the concept of the distance of a given EP in matrix space to the set of DPs. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this EP. 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 EPs that rely on perturbing a DP. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. Several optical systems are investigated to illustrate the theory.