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  • Letter
  • Open Access

Enhanced sensitivity in non-Hermitian systems at infernal points

Shu-Xuan Wang* and Zhongbo Yan†

  • Guangdong Provincial Key Laboratory of Magnetoelectric Physics and Devices, State Key Laboratory of Optoelectronic Materials and Technologies, School of Physics, Sun Yat-sen University, Guangzhou 510275, China

  • *Contact author: wangshx65@mail.sysu.edu.cn
  • †Contact author: yanzhb5@mail.sysu.edu.cn
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Phys. Rev. Research 7, L022037 – Published 19 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022037

Abstract

The emergence of exceptional points in non-Hermitian systems represents an intriguing phenomenon characterized by the coalescence of eigenenergies and eigenstates. When a system approaches an exceptional point, it exhibits a heightened sensitivity to perturbations compared to the conventional band degeneracy observed in Hermitian systems. This sensitivity, manifested in the splitting of the eigenenergies, is amplified as the order of the exceptional point increases. Infernal points constitute a unique subclass of exceptional points, distinguished by their order escalating with the expansion of the system's size. In this paper, we show that when a non-Hermitian system is at an infernal point, a perturbation of strength ε, which couples the two opposing boundaries of the system, causes the eigenenergies to split according to the law εk, where k is an integer proportional to the system's size. Utilizing the perturbation theory of Jordan matrices, we demonstrate that the exceptional sensitivity of the eigenenergies at infernal points to boundary-coupling perturbations is a ubiquitous phenomenon, irrespective of the specific form of the non-Hermitian Hamiltonians. Notably, we find that this phenomenon remains robust even when the system deviates substantially from the infernal point. The universal nature and robustness of this phenomenon suggest potential applications in enhancing sensor sensitivity.

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Phys. Rev. Research 7, L022037– Published 19 May, 2025
  • Received 28 January 2025
  • Revised 21 April 2025
  • Accepted 9 May 2025
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