PT‐Symmetric Two‐Photon Quantum Rabi Models

Abstract Two non‐Hermitian two‐photon quantum Rabi models (tpQRM) that exhibit parity‐time () symmetry are investigated: the biased tpQRM (btpQRM), where the qubit bias is purely imaginary, and the dissipative tpQRM (dtpQRM), where the two‐photon coupling is made imaginary to introduce dissipation. For both models, exact solutions are derived using Bogoliubov transformations. In the btpQRM, spectral collapse is identified at a critical coupling strength, with accompanying symmetry breaking that correlates with exceptional points (EPs) arising from coalescing eigenstates. A direct correspondence is established between ‐broken regions and the doubly degenerate points of the Hermitian tpQRM, and the effect of qubit bias is analyzed via an adiabatic approximation. In the dtpQRM, although no spectral collapse occurs, both EPs and Juddian‐type degeneracies are present, with distinct behaviors governed by parity conservation. Through biorthogonal fidelity susceptibility and c‐product, the nature of these two types of level crossings is successfully identified and characterized. Finally, the dynamical evolution of both models is compared, revealing fundamentally different pathways to steady states governed by their respective non‐Hermitian spectral structures. These results provide exact characterizations of ‐symmetric non‐Hermitian tpQRMs and may offer theoretical insights for future experimental realizations.