Critical spectrum of the anisotropic two-photon quantum Rabi model
arXiv:2412.20437 · doi:10.1103/PhysRevA.111.043706
Abstract
The anisotropic two-photon quantum Rabi model is studied using the Bogoliubov operator approach. The doubly degenerate exceptional states are identified through analytical methods. By adjusting the position of the last exceptional point belonging to two adjacent energy levels, we derive a condition for the absence of the discrete spectrum at the critical coupling where ``spectral collapse" occurs. In this special case, the spectrum becomes fully continuous above a threshold energy, with no bound states existing, whereas the ground state remains gapped in the general case. This also signals a quantum phase transition. More interestingly, we rigorously find that a finite number of bound states exist between two anisotropy dependent critical atomic frequencies, with infinitely many bound states beyond this frequency regime. In this manner, all issues in the two-photon quantum Rabi model are resolved.
arXiv comment12 pages, 12 figures,
References in corpus (31)
- Quantum nature of a strongly-coupled single quantum dot-cavity system
- Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
- Ultrastrong coupling regimes of light-matter interaction
- On the Integrability of the Rabi Model
- Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
- Exact solvability of the quantum Rabi models within Bogoliubov operators
- Generating and probing a two-photon Fock state with a single atom in a cavity
- Two-photon quantum Rabi model with superconducting circuits
- Semi-classical and quantum Rabi models: in celebration of 80 years
- Spectral collapse via two-phonon interactions in trapped ions
- Anisotropic Rabi model
- Two-photon Rabi model: Analytic solutions and spectral collapse
- Exact Solvability of the two-photon Rabi Hamiltonian
- Two-photon lasing by a single quantum dot in a high-Q microcavity
- A generalization of the quantum Rabi model: exact solution and spectral structure
- Ultrastrong coupling regime of non-dipolar light-matter interactions
- Polaron picture of the two-photon quantum Rabi model
- Exact real-time dynamics of the quantum Rabi model
- Critical Quantum Metrology in the Non-Linear Quantum Rabi Model
- On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
- Spectral Collapse in the two-photon quantum Rabi model
- Quantum Rabi-Stark model: Solutions and exotic energy spectra
- Solution of the two-mode quantum Rabi model using extended squeezed states
- Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study
- Multiple ground-state instabilities in the anisotropic quantum Rabi model
- Spectral determinant of the two-photon quantum Rabi model
- Hidden -algebraic structure in Rabi model and its 2-photon and two-mode generalizations
- A novel approach to the spectral problem in the two photon Rabi model
- Bound states of two-photon Rabi model at the collapse point
- Spectral continuum in the Rabi-Stark model
- Solving and Completing the Rabi-Stark Model in the Ultrastrong Coupling Regime