Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems
Exceptional points (EPs) are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points (DPs), at which only eigenen...
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| Format: | Article |
| Language: | English |
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American Physical Society
2022-09-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.4.033179 |
| _version_ | 1797210627921412096 |
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| author | Jan Wiersig |
| author_facet | Jan Wiersig |
| author_sort | Jan Wiersig |
| collection | DOAJ |
| description | Exceptional points (EPs) are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points (DPs), at which only eigenenergies degenerate. Here, we connect these two kinds of degeneracies by introducing the concept of the distance of a given EP in matrix space to the set of DPs. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this EP. A small distance therefore implies a weak spectral response to perturbations and a weak intensity response to excitations. This finding has profound consequences for physical realizations of EPs that rely on perturbing a DP. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. Several optical systems are investigated to illustrate the theory. |
| first_indexed | 2024-04-24T10:13:37Z |
| format | Article |
| id | doaj.art-226afd0f4bd54d7a839ea08e840e928d |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:13:37Z |
| publishDate | 2022-09-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-226afd0f4bd54d7a839ea08e840e928d2024-04-12T17:24:15ZengAmerican Physical SocietyPhysical Review Research2643-15642022-09-014303317910.1103/PhysRevResearch.4.033179Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systemsJan WiersigExceptional points (EPs) are non-Hermitian degeneracies in open quantum and wave systems at which not only eigenenergies but also the corresponding eigenstates coalesce. This is in strong contrast to degeneracies known from conservative systems, so-called diabolic points (DPs), at which only eigenenergies degenerate. Here, we connect these two kinds of degeneracies by introducing the concept of the distance of a given EP in matrix space to the set of DPs. We prove that this distance determines an upper bound for the response strength of a non-Hermitian system with this EP. A small distance therefore implies a weak spectral response to perturbations and a weak intensity response to excitations. This finding has profound consequences for physical realizations of EPs that rely on perturbing a DP. Moreover, we exploit this concept to analyze the limitations of the spectral response strength in passive systems. Several optical systems are investigated to illustrate the theory.http://doi.org/10.1103/PhysRevResearch.4.033179 |
| spellingShingle | Jan Wiersig Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems Physical Review Research |
| title | Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems |
| title_full | Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems |
| title_fullStr | Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems |
| title_full_unstemmed | Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems |
| title_short | Distance between exceptional points and diabolic points and its implication for the response strength of non-Hermitian systems |
| title_sort | distance between exceptional points and diabolic points and its implication for the response strength of non hermitian systems |
| url | http://doi.org/10.1103/PhysRevResearch.4.033179 |
| work_keys_str_mv | AT janwiersig distancebetweenexceptionalpointsanddiabolicpointsanditsimplicationfortheresponsestrengthofnonhermitiansystems |