Revisiting the hierarchical construction of higher-order exceptional points

TL;DR

This paper explores a new approach to constructing higher-order exceptional points in non-Hermitian systems, providing a generalized formula for spectral response and analyzing robustness against perturbations.

Contribution

It introduces a novel method based on Hamiltonian nilpotency for creating higher-order exceptional points and derives a simple spectral response formula.

Findings

Derived a general formula for spectral response strength

Analyzed robustness under nongeneric perturbations

Illustrated results with a specific example

Abstract

Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describing open quantum or wave systems have a variety of potential applications in particular in optics and photonics. However, the experimental realization is notoriously difficult. Recently, Q. Zhong et al. [Phys. Rev. Lett. 125, 203602 (2020)] have introduced a robust construction where a unidirectional coupling of two subsystems having exceptional points of the same order leads generically to a single exceptional point of twice the order. Here, we investigate this scheme in a different manner by exploiting the nilpotency of the traceless part of the involved Hamiltonians. We generalize the scheme and derive a simple formula for the spectral response strength of the composite system hosting a higher-order exceptional point. Its relation to the spectral response strengths of the subsystems is discussed. Moreover, we investigate nongeneric perturbations. The results are illustrated with an example.