Revisiting the hierarchical construction of higher-order exceptional points

• URL: http://arxiv.org/abs/2210.04459v2
• Date: Wed, 4 Jan 2023 07:39:07 GMT
• Title: Revisiting the hierarchical construction of higher-order exceptional points
• Authors: Jan Wiersig
• Abstract summary: Higher-order exceptional points in the spectrum of non-Hermitian Hamiltonians describe open quantum or wave systems. We derive a formula for the spectral response strength of the composite system hosting a higher-order exceptional point.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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