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

TL;DR

This paper introduces rotation-time (${\cal{RT}}$) symmetry in open bosonic systems, demonstrating that such systems can have real spectra and exceptional points without ${\cal{PT}}$ symmetry, expanding the understanding of non-Hermitian spectral properties.

Contribution

The study reveals a new ${\cal{RT}}$ symmetry in bosonic systems, providing methods to identify and construct ${\cal{RT}}$-symmetric Hamiltonians and analyzing their spectral singularities.

Findings

${\cal{RT}}$-symmetric Hamiltonians can have real spectra.

Spectral singularities occur at symmetry-breaking points.

Provided rules for constructing ${\cal{RT}}$-symmetric Hamiltonians.

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.