We analyse two quantum systems with hidden parity-time ([Formula: see text]) symmetry: one is an optical device, whereas another is a superconducting microwave-frequency device. To investigate their symmetry, we introduce a damping frame (DF), in which loss and gain terms for a given Hamiltonian are balanced. We show that the non-Hermitian Hamiltonians of both systems can be tuned to reach an exceptional point (EP), i.e., the point in parameter space at which a transition from broken to unbroken hidden [Formula: see text] symmetry takes place. We calculate a degeneracy of a Liouvillian superoperator, which is called the Liouvillian exceptional point (LEP), and show that, in the optical domain, LEP is equivalent to EP obtained from the non-Hermitian Hamiltonian (HEP). We also report breaking the equivalence between LEP and HEP by a non-zero number of thermal photons for the microwave-frequency system.

Institute of Spintronics and Quantum Information Faculty of Physics Adam Mickiewicz University 61 614 Poznań Poland

RCPTM Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences 17 listopadu 12 771 46 Olomouc Czech Republic

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Sci Rep. 2023 Oct 6;13(1):16852. doi: 10.1038/s41598-023-43997-9. PubMed

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