[Paper Review] Sensitivity of topological edge states in a non-Hermitian dimer chain

Zhiwei Guo, Tengzhou Zhang+3 more|arXiv (Cornell University)|Jul 7, 2020

Quantum Mechanics and Non-Hermitian Physics58 references4 citations

TL;DR

This paper proposes a non-Hermitian dimer chain with engineered gain and loss to stabilize topological edge states at exceptional points (EPs), restoring topological protection despite near-field coupling. By tuning the EP, the system achieves high sensitivity to external perturbations at the edges while remaining robust against internal structural defects, enabling a novel class of topological sensors with enhanced precision.

ABSTRACT

Photonic topological edge states in one-dimensional dimer chains have long been thought to be robust to structural perturbations by mapping the topological Su-Schrieffer-Heeger model of a solid-state system. However, the edge states at the two ends of a finite topological dimer chain will interact as a result of near-field coupling. This leads to deviation from topological protection by the chiral symmetry from the exact zero energy, weakening the robustness of the topological edge state. With the aid of non-Hermitian physics, the splitting frequencies of edge states can be degenerated again and topological protection recovered by altering the gain or loss strength of the structure. This point of coalescence is known as the exceptional point (EP). The intriguing physical properties of EPs in topological structures give rise to many fascinating and counterintuitive phenomena. In this work, based on a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators, we propose theoretically and verify experimentally that the sensitivity of topological edge states is greatly affected when the system passes through the EP. Using the EP of a non-Hermitian dimer chain, we realize a new sensor that is sensitive to perturbation at the end of the structure and yet topologically protected from internal perturbation. Our demonstration of a non-Hermitian topological structure with an EP paves the way for the development of novel sensors that are not sensitive to internal manufacturing errors but are highly sensitive to changes in the external environment.

Motivation & Objective

• To address the loss of topological protection in finite dimer chains due to near-field coupling between edge states.
• To explore how non-Hermitian physics, particularly exceptional points (EPs), can restore topological robustness.
• To design and experimentally verify a topological sensor that is sensitive to external environmental changes but resilient to internal manufacturing imperfections.
• To demonstrate the feasibility of using EPs in non-Hermitian systems for enhanced sensing applications in photonic topological structures.

Proposed method

• Theoretical modeling of a finite non-Hermitian dimer chain composed of ultra-subwavelength resonators with asymmetric gain and loss.
• Use of the Su-Schrieffer-Heeger (SSH) model adapted to non-Hermitian systems to describe topological edge states.
• Engineering the system parameters to reach an exceptional point (EP), where eigenfrequencies coalesce, restoring topological protection.
• Numerical simulation and analytical derivation of the splitting frequencies of edge states as a function of gain-loss strength.
• Experimental realization using microwave resonators to validate the theoretical predictions of edge state sensitivity at the EP.
• Characterization of the system's response to external perturbations at the chain ends versus internal structural variations.

Experimental results

Research questions

• RQ1 How does near-field coupling between edge states in a finite dimer chain compromise topological protection?
• RQ2 Can exceptional points (EPs) in a non-Hermitian dimer chain restore topological robustness by degenerating edge state splitting frequencies?
• RQ3 To what extent can the system maintain topological protection while exhibiting high sensitivity to external perturbations at the chain ends?
• RQ4 How does the interplay between gain and loss strength affect the localization and sensitivity of topological edge states?
• RQ5 Can a non-Hermitian topological structure be engineered to function as a robust yet highly sensitive sensor?

Key findings

• Near-field coupling in finite dimer chains causes splitting of topological edge states from exact zero energy, breaking chiral symmetry and weakening topological protection.
• At the exceptional point (EP), the splitting frequencies of edge states coalesce, restoring topological protection despite coupling.
• The system exhibits high sensitivity to external perturbations at the chain ends, while remaining robust against internal structural defects.
• Experimental results in a microwave setup confirm the theoretical prediction of enhanced edge state sensitivity at the EP.
• The non-Hermitian dimer chain enables a new sensing paradigm: topologically protected against internal errors but highly responsive to external changes.
• The sensitivity of the edge states is maximized when the system operates precisely at the EP, demonstrating a trade-off between robustness and responsiveness.