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.

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

References in corpus (6)

• Analytical method of spectra calculations in the Bargmann representation
• An exactly solvable system from quantum optics
• Note on the Analytical Solution of the Rabi Model
• Continued Fractions and the Rabi Model
• A novel approach to the spectral problem in the two photon Rabi model
• Bound states of two-photon Rabi model at the collapse point

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
• Critical Spectrum and Quantum Criticality in the Two-Photon Rabi-Stark Model
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models