Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation

• URL: http://arxiv.org/abs/2606.04386v1
• Date: Wed, 03 Jun 2026 03:02:32 GMT
• Title: Optimizing the Sensitivity-Noise Trade-off in Non-Hermitian Sensing via Off-Exceptional-Deficiency Operation
• Abstract summary: spectral singularities simultaneously amplify both the signal and environmental noise.<n>We show that the "Off-ED" framework reconciles extreme sensitivity with robust noise immunity.<n>Our findings establish the Off-ED framework as a paradigm for next-generation topological sensors.
• Score: 4.49555689737163
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A central challenge in non-Hermitian sensing is that spectral singularities simultaneously amplify both the signal and environmental noise. We address this predicament in a double-chain Hatano-Nelson model featuring unidirectional interlayer coupling. At the exceptional deficiency (ED) limit, the system exhibits a macroscopically degenerate complex spectrum and a pronounced non-Hermitian skin effect (NHSE), yielding a sensitivity that scales exponentially with lattice size $N$ while remaining robust across a six-order-of-magnitude detuning range. By introducing diagonal spatial disorder, we demonstrate that the NHSE is progressively suppressed, whith eigenspace cosine similarity analysis quantifying a well-defined fault-tolerance threshold. To reconcile the sensitivity-noise trade-off, we delineate "At-ED" and "Off-ED" operating regimes. While the At-ED configuration imposes fractional-order noise amplification (SNR $\propto δ^{-1/2}$) that saturates at a suboptimal plateau, migrating to the Off-ED regime eliminates this geometric singularity and restores a linear scaling law (SNR $\propto δ^{-1}$), achieving an SNR enhancement of several orders of magnitude. Crucially, this improvement is achieved while fully preserving the exponential sensitivity scaling, albeit at a slightly reduced absolute sensitivity compared to the strict At-ED limit. Our findings establish the Off-ED framework as a concrete paradigm for next-generation topological sensors that reconcile extreme sensitivity with robust noise immunity.

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