The Role of Exceptional Points and Transmission Peak Degeneracies in Non-Hermitian Sensing

TL;DR

This paper develops a unified theoretical framework for transmission peak degeneracies (TPDs) in non-Hermitian sensing, demonstrating their advantages over exceptional points (EPs) in robustness and practical sensor design.

Contribution

It introduces a comprehensive theory of 2D TPDs, maps their parameter space, and validates the approach with a tunable cavity-magnonics platform, advancing non-Hermitian sensor development.

Findings

TPDs retain square-root splitting under nuisance parameter drift.

Identified TPD configurations that minimize impact of nuisance drift.

Validated theory with experimental platform exploring various symmetry regimes.

Abstract

Transmission peak degeneracies (TPDs) have emerged as a promising alternative to exceptional points (EPs) for non-Hermitian sensing, providing square-root frequency splitting without the eigenbasis collapse and associated noise amplification that limit EP sensors. However, existing treatments of TPDs remain fragmented, lacking a unified theoretical framework, systematic figures of merit, or design principles for practical implementation. Here, we develop a comprehensive theory of two-dimensional TPDs that clarifies their relationship to EPs, maps their locations in parameter space, and provides analytic figures of merit for sensor design. We validate our theory using a tunable cavity-magnonics platform with in situ control of mode frequency, dissipation, and complex coupling via an effective synthetic gauge field. Our platform enables systematic exploration of six representative EP-TPD configurations spanning PT-symmetric, anti-PT-symmetric and anyonic-PT-symmetric regimes. Crucially, we show that TPDs, unlike EPs, retain square-root splitting even under nuisance parameter drift through generalized transmission extrema degeneracies (TEDs). We further identify specific robust TPD configurations that minimize the impact of nuisance drift. These findings establish a unified theoretical and experimental framework for TPD-based non-Hermitian sensing.