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