On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations

Abstract

We study the solvability of the time-independent matrix Schrödinger differential equations of the quantum Rabi model and its 2-photon and two-mode generalizations in Bargmann Hilbert spaces of entire functions. We show that the Rabi model and its 2-photon and two-mode analogs are quasi-exactly solvable. We derive the exact, closed-form expressions for the energies and the allowed model parameters for all the three cases in the solvable subspaces. Up to a normalization factor, the eigenfunctions for these models are given by polynomials whose roots are determined by systems of algebraic equations.

LaTex 16 pages. Some modifications and addition of references. Version to appear in J. Math. Phys

References in corpus (4)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• On the spectrum of a class of quantum models
• Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian

Cited by in corpus (34)

• The quantum Rabi model: solution and dynamics
• One-Dimensional Quasi-Exactly Solvable Schrödinger Equations
• Two-photon Rabi model: Analytic solutions and spectral collapse
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Differential equations for singular values of products of Ginibre random matrices
• Solution of the two-mode quantum Rabi model using extended squeezed states
• Hidden symmetry and tunnelling dynamics in asymmetric quantum Rabi models
• $\mathcal{P}\mathcal{T}$ phase transition in open quantum systems with Lindblad dynamics
• Analytical energy spectrum for hybrid mechanical systems
• Quantum phase transitions for an integrable quantum Rabi-like model with two interacting qubits
• Generalized quantum Rabi model with both one- and two-photon terms: A concise analytical study
• Dark-like states for the multi-qubit and multi-photon Rabi models
• Cross-cavity quantum Rabi model
• Spectral determinant of the two-photon quantum Rabi model
• Generalized adiabatic approximation to the quantum Rabi model
• A continued fraction based approach for the Two-photon Quantum Rabi Model
• The mixed quantum Rabi model
• Generalized Rabi models: diagonalization in the spin subspace and differential operators of Dunkl type
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Two-photon Rabi-Stark model
• Level crossings and new exact solutions of the two-photon Rabi model
• $Z_N$ symmetric chiral Rabi model: a new $N$-level system
• Bound states of two-photon Rabi model at the collapse point
• Physical background for parameters of the quantum Rabi model
• Hidden symmetry in the biased Dicke model
• On the 2-mode and $k$-photon quantum Rabi models
• Thermodynamic Limit in the Two-qubit Quantum Rabi Model with Spin-Spin Coupling
• Critical spectrum of the anisotropic two-photon quantum Rabi model
• Unified approach to the nonlinear Rabi models
• The asymmetric quantum Rabi model and generalised Pöschl-Teller potentials
• A unified treatment of polynomial sectors and constraint polynomials of the Rabi models
• The Yang-Baxter paradox
• Hidden $sl(2)-$Symmetry of the Generalized Landau-Zener Vibronic Model
• Polynomial deformations of $sl(2)$ and unified algebraic framework for solutions of a class of spin models