Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{PT}$ symmetry

• URL: http://arxiv.org/abs/2008.06539v2
• Date: Thu, 19 Nov 2020 19:46:03 GMT
• Title: Rotation-time symmetry in bosonic systems and the existence of exceptional points in the absence of $\mathcal{PT}$ symmetry
• Authors: Ewelina Lange and Grzegorz Chimczak and Anna Kowalewska-Kud{\l}aszyk and Karol Bartkiewicz
• Abstract summary: We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ($calPT$) symmetric in special cases only.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time (${\cal{PT}}$) symmetric in special cases only. Systems exhibiting this symmetry are characterised by real-valued energy spectra and can display exceptional points, where a symmetry-breaking transition occurs. We demonstrate that there is a more general type of symmetry, i.e., rotation-time (${\cal{RT}}$) symmetry. We observe that ${\cal{RT}}$-symmetric non-Hermitian Hamiltonians exhibit real-valued energy spectra which can be made singular by symmetry breaking. To calculate the spectra of the studied bosonic non-diagonalisable Hamiltonians we apply diagonalisation methods based on bosonic algebra. Finally, we list a versatile set rules allowing to immediately identifying or constructing ${\cal{RT}}$-symmetric Hamiltonians. We believe that our results on the ${\cal{RT}}$-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the ${\cal{PT}}$-symmetric systems.

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