Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.13434 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914953583132672 |
|---|---|
| author | Grom, Daniel Kullig, Julius Röntgen, Malte Wiersig, Jan |
| author_facet | Grom, Daniel Kullig, Julius Röntgen, Malte Wiersig, Jan |
| contents | Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding eigenvectors simultaneously coalesce. These coalescing eigenvalues typically exhibit a strong response to small perturbations which can be useful for sensor applications. A so-called generic perturbation with strength $ε$ changes the eigenvalues proportional to the n-th root of $ε$. A different eigenvalue behavior under perturbation is called non-generic. An understanding of the behavior of the eigenvalues for various types of perturbations is desirable and also crucial for applications. We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points, i.e. n > 2. To highlight the relevance of non-generic perturbations and to give an interpretation for their occurrence, we consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror. Furthermore, the saturation effect occurring for cavity-selective sensing in such a system is naturally explained within the graph-theoretical picture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_13434 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Graph-theoretical approach to the eigenvalue spectrum of perturbed higher-order exceptional points Grom, Daniel Kullig, Julius Röntgen, Malte Wiersig, Jan Quantum Physics Other Condensed Matter Optics Exceptional points are special degeneracy points in parameter space that can arise in (effective) non-Hermitian Hamiltonians describing open quantum and wave systems. At an n-th order exceptional point, n eigenvalues and the corresponding eigenvectors simultaneously coalesce. These coalescing eigenvalues typically exhibit a strong response to small perturbations which can be useful for sensor applications. A so-called generic perturbation with strength $ε$ changes the eigenvalues proportional to the n-th root of $ε$. A different eigenvalue behavior under perturbation is called non-generic. An understanding of the behavior of the eigenvalues for various types of perturbations is desirable and also crucial for applications. We advocate a graph-theoretical perspective that contributes to the understanding of perturbative effects on the eigenvalue spectrum of higher-order exceptional points, i.e. n > 2. To highlight the relevance of non-generic perturbations and to give an interpretation for their occurrence, we consider an illustrative example, a system of microrings coupled by a semi-infinite waveguide with an end mirror. Furthermore, the saturation effect occurring for cavity-selective sensing in such a system is naturally explained within the graph-theoretical picture. |
| title | Graph-theoretical approach to the eigenvalue spectrum of perturbed higher-order exceptional points |
| topic | Quantum Physics Other Condensed Matter Optics |
| url | https://arxiv.org/abs/2409.13434 |