Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points

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 $\epsilon$, which couples the two opposing boundaries of the system, causes the eigenenergies to split according to the law $\sqrt[k]{\epsilon}$, 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.

• The paper shows non-Hermitian systems exhibit super-enhanced sensitivity at infernal points, where boundary perturbations split eigenenergies via a power law (ε^(1/k)).
• The study finds this sensitivity is robust across deviations from the exact infernal point, broadening potential experimental applications.
• The findings are applicable to a wide class of one-dimensional non-Hermitian systems and suggest potential for enhanced precision sensing technologies.

Overview of Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points

The paper authored by Shu-Xuan Wang and Zhongbo Yan, titled "Super-enhanced Sensitivity in Non-Hermitian Systems at Infernal Points," explores the study of non-Hermitian systems, particularly focusing on the behavior of these systems at exceptional points (EPs). Non-Hermitian Hamiltonians, which deviate from the Hermitian constraint commonly assumed in quantum mechanics, describe open systems effectively and exhibit interesting phenomena, including the presence of EPs where eigenstates and eigenenergies coalesce. Exceptional points have been recognized for their enhanced sensitivity to perturbations, promising applications in precision sensing. The paper further investigates a subclass of EPs, termed 'infernal points' (IPs), which are high-order EPs that emerge in non-Hermitian lattice systems under open boundary conditions.

Key Findings:

1. Splitting Behavior at Infernal Points: The study identifies that at an IP, a perturbation of strength $\epsilon$ coupling the boundaries of a system causes the eigenenergies to split according to the law $\sqrt[k]{\epsilon}$, with $k$ being proportional to the system's size. This finding illustrates exceptional sensitivity compared to Hermitian systems, where energy splits linearly with perturbation strength.
2. Robustness Across System Deviations: Utilizing the perturbation theory for Jordan matrices, the authors illustrate that this sensitivity to boundary-coupling perturbations is a robust phenomenon in non-Hermitian systems. Notably, the sensitivity persists even if the system deviates slightly from an IP, expanding potential experimental applicability.
3. General Applicability: The authors extend their model beyond the Hatano-Nelson model used initially, encapsulating a wider class of one-dimensional non-Hermitian systems and suggesting the phenomenon's pervasive nature across different forms of non-Hermitian Hamiltonians.
4. Theoretical Condition for Maximum Splitting: The work establishes a theoretical condition on perturbations that result in maximal energy splitting, emphasizing that precisely tuned boundary-coupling perturbations can achieve the observed super-enhanced sensitivity.

Implications and Future Directions:

• Enhanced Sensor Design:

The identified property of IPs could significantly impact sensor technology by leveraging the sensitivity of eigenenergy responses to detect environmental perturbations at scales previously unattainable in Hermitian systems.

• Potential for Experimental Realization:

The authors argue that observable manifestations of this phenomenon are feasible with current experimental techniques, particularly in systems exhibiting strong non-Hermitian skin effects. Realizing the anticipated exceptional sensitivity could pave the way for novel experimental setups and applications.

• Theoretical Development:

As the detailed understanding of the perturbation response at IPs develops, future theoretical work might focus on multi-dimensional systems and varying boundary conditions to explore the versatility of the observed phenomenon.

The paper contributes significant insights into non-Hermitian physics, suggesting robust methodologies for exploiting high-sensitivity measurements. While methodological rigor supports these claims, the practical realization aligns well with current advancements in non-Hermitian system experiments, promising tangible developments in the field's application scope.