Solution of the two-mode quantum Rabi model using extended squeezed states

Abstract

The two-mode quantum Rabi model with bilinear coupling is studied using extended squeezed states. We derive $G$-functions for each Bargmann index $q$% . They share a common structure with the $G$-function of the one-photon and two-photon quantum Rabi models. The regular spectrum is given by zeros of the $G$-function while the conditions for the presence of doubly degenerate (exceptional) eigenvalues are obtained in closed form through the lifting property. The simple singularity structure of the $G$-function allows to draw conclusions about the distribution of eigenvalues along the real axis and to understand the spectral collapse phenomenon when the coupling reaches a critical value.

6 pages, 2 figures

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• Frequency conversion in ultrastrong cavity QED
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• Error-Tolerant Amplification and Simulation of the Ultrastrong-Coupling Quantum Rabi Model
• Dark-like states for the multi-qubit and multi-photon Rabi models
• First-order and continuous quantum phase transitions in the anisotropic quantum Rabi-Stark model
• Double degeneracy associated with hidden symmetries in the asymmetric two-photon Rabi model
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• Cross-cavity quantum Rabi model
• Hidden $sl(2)$-algebraic structure in Rabi model and its 2-photon and two-mode generalizations
• The mixed quantum Rabi model
• Bound states of two-photon Rabi model at the collapse point
• On the 2-mode and $k$-photon quantum Rabi models
• Unified approach to the nonlinear Rabi models
• Critical spectrum of the anisotropic two-photon quantum Rabi model
• General symmetry operators of the asymmetric quantum Rabi model
• Quantum criticality driven by the cavity coupling in Rabi-dimer model
• Approximating the two-mode two-photon Rabi model
• Tripartite quantum Rabi model with trapped Rydberg ions
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model