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 typi..., , , # Noise-resilient exceptional point sensing with immunity to undesired perturbations

## Description of files and variables

### `allan_variances.mat`

This file contains Allan variance and Allan deviation data from five runs each for five frequency offsets, each consisting of 20,000 points collected over 3 * 192.01 seconds. The frequency offsets are:

* 1.744 GHz (50 MHz away)
* 1.784 GHz (10 MHz away)
* 1.789 GHz (5 MHz away)
* 1.792 GHz (2 MHz away)
* 1.793 GHz (1 MHz away)

#### Notes

* The first four frequencies lie within the sublinear scaling range.
* All measurements share the same tau values, determined by the total measurement duration.

#### Variables

##### `avar_i_j`

* The j-th measurement run of the Allan variance for the i-th frequency offset (in MHz from the SIP).
* Each variable is a vector over tau.

##### `tau`

* Shared across all files.
* Determined by the total measurement interval.

##### `avar_i`

* Matrix of Allan variances for frequency offset i.
* 5 rows, on...,