Spectral determinant of the two-photon quantum Rabi model

Abstract

The various generalized spectral determinants (G-functions) of the two-photon quantum Rabi model are analyzed with emphasis on the qualitative aspects of the regular spectrum. Whereas all of them yield at least a subset of the exact regular eigenvalues, only the G-function proposed by Chen et al. in 2012 exhibits an explicitly known pole structure which dictates the approach to the collapse point. We derive this function rigorously employing the ${\mathbb{Z}}_4$-symmetry of the model and show that its zeros correspond to the complete regular spectrum.

arXiv commentSection 2.2 of the published version corrected (correction has been sent to Publisher)

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Cited by in corpus (7)

• Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
• Spectral continuum in the Rabi-Stark model
• Critical quantum metrology in a stabilized two-photon Rabi model
• Critical spectrum of the anisotropic two-photon quantum Rabi model
• Unified approach to the nonlinear Rabi models
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• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models