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Temporal Localisation of Waves from Imaginary Line-Gap Topology

  • Carlos Camacho
  • Tom Sheppard
  • Joshua Feis
  • Oliver Ashfield
  • Alexander Szameit
  • Frank Schindler
  • Hannah M. Price
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Abstract

For non-Hermitian Hamiltonians, gain, loss, and non-reciprocity produce complex eigenvalues which, in turn, facilitate different kinds of topological phases. One example is the imaginary line-gap phase, where eigenvalues cannot lie on the real line. This notion was recently shown to explain the robust temporal localisation of waves in photonic quantum walks and time-varying metamaterials. In these systems, waves localise around a time interface between topologically inequivalent mediums. At the core of this phenomenon is a 𝒫𝒯-symmetric two-mode model, where the non-trivial topology arises due to the β„€2 classification of the AI symmetry class. In this work, we study two-mode models in all non-Hermitian symmetry classes. We find that robust temporal localisation generically follows as a physical consequence of imaginary line-gap topology according to a simple diagnostic: at least one of time-reversal symmetry (𝒯hspace0.05em2 = 1) and particle-hole symmetry (π’ž2 = 1) must be present. Our results provide a comprehensive symmetry-based guide to the observation of the topologically protected temporal localisation of waves.

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Cite

BibTeXRIS
BibTeX
@misc{camacho2026temporal,
  title = {{Temporal Localisation of Waves from Imaginary Line-Gap Topology}},
  author = {Carlos Camacho and Tom Sheppard and Joshua Feis and Oliver Ashfield and Alexander Szameit and Frank Schindler and Hannah M. Price},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.11577},
  eprint = {2609.11577},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.11577},
}
RIS
TY  - UNPB
TI  - Temporal Localisation of Waves from Imaginary Line-Gap Topology
AU  - Carlos Camacho
AU  - Tom Sheppard
AU  - Joshua Feis
AU  - Oliver Ashfield
AU  - Alexander Szameit
AU  - Frank Schindler
AU  - Hannah M. Price
PY  - 2026
DA  - 2026/09/11
PB  - arXiv
DO  - 10.48550/arxiv.2609.11577
UR  - https://arxiv.org/abs/2609.11577
AB  - For non-Hermitian Hamiltonians, gain, loss, and non-reciprocity produce complex eigenvalues which, in turn, facilitate different kinds of topological phases. One example is the imaginary line-gap phase, where eigenvalues cannot lie on the real line. This notion was recently shown to explain the robust temporal localisation of waves in photonic quantum walks and time-varying metamaterials. In these systems, waves localise around a time interface between topologically inequivalent mediums. At the core of this phenomenon is a 𝒫𝒯-symmetric two-mode model, where the non-trivial topology arises due to the β„€_2 classification of the AI symmetry class. In this work, we study two-mode models in all non-Hermitian symmetry classes. We find that robust temporal localisation generically follows as a physical consequence of imaginary line-gap topology according to a simple diagnostic: at least one of time-reversal symmetry (𝒯^hspace0.05em2 = 1) and particle-hole symmetry (π’ž^2 = 1) must be present. Our results provide a comprehensive symmetry-based guide to the observation of the topologically protected temporal localisation of waves.
ER  -