Sensing with Non-Hermitian Degeneracies Beyond Exceptional Points

Harnessing the characteristic square-root frequency splitting of exceptional points (EPs) permits sensor designs that outperform conventional, linear-scaling devices. However, most practical EP sensors amplify noise externally, through active gain components, and intrinsically, through the eigenbasis collapse at EPs, limiting signal-to-noise ratio. We circumvent these tradeoffs by distinguishing EPs from transmission spectrum degeneracies observed in experiment. We demonstrate that transmission peak degeneracies (TPDs) reproduce square-root splitting while preserving linearity, passive operation, and a complete eigenbasis. We develop the theory of TPDs and validate it experimentally using a tunable cavity-magnonics platform with in situ control of mode frequency, dissipation, and complex coupling via a synthetic gauge field, realizing six representative EP–TPD pairs spanning PT, anti-PT , and anyonic-PT regimes. The phase tunable synthetic gauge field allows TPDs to be configured to sense electric field, magnetic field, or both jointly. We introduce analytic figures of merit beyond the Petermann factor to identify the best TPD candidates for robust sensing under these conditions. Our results uncover unexplored classes of TPDs, unify EP and TPD theory, and establish design principles for noise resilient non-Hermitian sensors.