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

Abstract

We study symmetries of open bosonic systems in the presence of laser pumping. Non-Hermitian Hamiltonians describing these systems can be parity-time ($\mathcal{P}\mathcal{T}$) 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 ($\mathcal{R}\mathcal{T}$) symmetry. We observe that $\mathcal{R}\mathcal{T}$-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 $\mathcal{R}\mathcal{T}$-symmetric Hamiltonians. We believe that our results on the $\mathcal{R}\mathcal{T}$-symmetric class of bosonic systems and their spectral singularities can lead to new applications inspired by those of the $\mathcal{P}\mathcal{T}$-symmetric systems.

9 pages, 3 figures. This is a preprint of an article published in Scientific Reports. The final authenticated version is available online at: https://doi.org/10.1038/s41598-020-76787-8

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Cited by in corpus (7)

• Generating high-order quantum exceptional points in synthetic dimensions
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• The effect of thermal photons on exceptional points in coupled resonators
• Detection of unbroken phase of non-Hermitian system via Hermitian factorization surface
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Exceptional point in self-consistent Markovian master equations
• Localization with non-Hermitian off-diagonal disorder