Noise-resilient exceptional point sensing with immunity to undesired perturbations

Exceptional point degeneracies (EPDs) are non-Hermitian singularities where eigenvalues and their corresponding eigenvectors coalesce. When a small perturbation is induced, the eigenvalue detuning from an EPD follows a root sublinear expansion, which provides a means of enhancing the sensitivity (frequency shift) of resonant-based sensors. On the downside, resonant-based sensors are susceptible to cavity imperfections, local mechanical disturbances (temperature variations, vibrations), and other experimental uncertainties. Here, we overcome this problem by experimentally implementing passive periodic microwave metamaterials with non-resonant EPDs (NR-EPD) occurring in their Bloch spectrum. We demonstrate a sublinear variation of the reflectance near NR-EPDs to a specific class of (global) perturbations and propose its usage for ultra-sensitive sensing that is immune to undesired (local) perturbations. Importantly, the sensitivity is shielded from technical or fundamental noise that typically degrades the signal-to-noise performance of resonant EPDs.

例外简并点（Exceptional Point Degeneracies, EPDs）是一类非厄米奇异点，此时本征值与其对应的本征向量会发生简并重合。当引入微小微扰时，偏离例外简并点的本征值失谐量服从根型亚线性展开关系，这为提升基于谐振的传感器的灵敏度（频移量）提供了可行途径。但此类基于谐振的传感器存在明显局限：其易受腔体缺陷、局部机械扰动（如温度波动、振动）以及其他实验不确定性因素的影响。本研究通过实验构建无源周期性微波超材料，该材料的布洛赫谱中存在非谐振型例外简并点（non-resonant EPD, NR-EPD），以此解决上述问题。我们观测到，在非谐振型例外简并点附近，反射率对特定类别的（全局）微扰呈现亚线性变化关系，并提出将其应用于可抵御非预期（局部）微扰的超灵敏传感场景。尤为重要的是，该方案的灵敏度可免受技术噪声或本征噪声的影响——而这类噪声通常会劣化基于谐振型例外简并点的传感器的信噪比性能。