A generalization of the quantum Rabi model: exact solution and spectral structure

Abstract

We consider a generalization of the quantum Rabi model where the two-level system and the single-mode cavity oscillator are coupled by an additional Stark-like term. By adapting a method recently introduced by Braak [Phys. Rev. Lett. {\bf 107}, 100401 (2011)], we solve the model exactly. The low-lying spectrum in the experimentally relevant ultrastrong and deep strong regimes of the Rabi coupling is found to exhibit two striking features absent from the original quantum Rabi model: avoided level crossings for states of the same parity and an anomalously rapid onset of two-fold near-degenerate levels as the Rabi coupling increases.

27 pages, 8 figures, published version, including added Corrigendum (J. Phys. A: Math. Theor. 56, 345302 (2023)) with corrected Eqs. (39) and (40), and new figures replacing Figs. 4 and 6. The conclusions drawn in the paper remain unchanged and valid

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• Symmetry breaking patterns, tricriticalities and quadruple points in quantum Rabi model with bias and nonlinear interaction
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• Combining Squeezing and Transition Sensitivity Resources for Quantum Metrology by Asymmetric Non-Linear Rabi model
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