Multiple ground-state instabilities in the anisotropic quantum Rabi model

Abstract

In this work, the anisotropic variant of the quantum Rabi model with different coupling strengths of the rotating and counter-rotating wave terms is studied by the Bogoliubov operator approach. The anisotropy preserves the parity symmetry of the original model. We derive the corresponding $G$-function, which yields both the regular and exceptional eigenvalues. The exceptional eigenvalues correspond to the crossing points of two energy levels with different parities and are doubly degenerate. We find analytically that the ground-state and the first excited state can cross several times, indicating multiple first-order phase transitions as function of the coupling strength. These crossing points are related to manifest parity symmetry of the Hamiltonian, in contrast to the level crossings in the asymmetric quantum Rabi model which are caused by a hidden symmetry.

arXiv comment8 pages, 5 figures

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• Multiple single-photon generations in three-level atoms coupled to cavity with non-Markovian effects
• Superradiant phase transitions in the quantum Rabi model: Overcoming the no-go theorem through anisotropy
• Hidden symmetry operators for asymmetric generalised quantum Rabi models
• Spectral continuum in the Rabi-Stark model
• Critical spectrum of the anisotropic two-photon quantum Rabi model
• General symmetry operators of the asymmetric quantum Rabi model
• A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
• Nonclassical correlations and quadrature squeezing of photons in anisotropic quantum Rabi-Stark model
• Emergence of Rich Dissipative Phases in the Anisotropic Quantum Rabi Model Driven by the $A^2$ Term
• Nonclassical Photon-Bundle Correlations in Quantum Rabi Models