On the Integrability of the Rabi Model

Abstract

The exact spectrum of the Rabi hamiltonian is analytically found for arbitrary coupling strength and detuning. I present a criterion for integrability of quantum systems containing discrete degrees of freedom which shows that in this case a finite symmetry group may entail integrability, even without the presence of conserved charges beyond the hamiltonian itself. Moreover, I introduce and solve a natural generalization of the Rabi model which has no symmetries and is therefore probably the smallest non-integrable physical system.

7 pages, 4 figures, figure captions corrected

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• Anisotropic Rabi model with two-photon relaxation
• Amplitude modulated Bloch oscillations of photon probability distribution in a cavity-atom system
• The Yang-Baxter paradox
• Dispersive regime of multiphoton qubit-oscillator interactions
• On analytic solutions of the driven, 2-photon and two-mode quantum Rabi models
• Parity symmetry and parity breaking in the quantum Rabi model with addition of Ising interaction
• Impact of micromotion and field-axis misalignment on the excitation of Rydberg states of ions in a Paul trap
• Approximate controllability of the Jaynes-Cummings dynamics
• Frustrated Rydberg Atom Arrays Meet Cavity-QED: Emergence of the Superradiant Clock Phase
• Solving and Completing the Rabi-Stark Model in the Ultrastrong Coupling Regime
• Dynamic sensitivity of quantum Rabi model with quantum criticality
• Spin Phonon Relaxation Dynamics from a Conical Intersection of Trapped Rydberg Ions
• Unveiling environmental entanglement in strongly dissipative qubits
• GHZ-like states in the Qubit-Qudit Rabi Model
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• Extending third quantization with commuting observables: a dissipative spin-boson model
• The justification of 'Two-Level Approximation' in strong light-matter interaction
• Optimal Dynamical Gauge in the Quantum Rabi Model
• Multilevel Quantum Rabi Models
• Loss of integrability in a system with two-photon interactions
• Phase-Space Topology in a Single-Atom Synthetic Dimension
• From Few to Many Emitters Cavity QED: Energy Levels and Emission Spectra From Weak to Deep-Strong Coupling
• Non-Gaussian Phase Transition and Cascade of Instabilities in the Dissipative Quantum Rabi Model
• Comparison of Quantum and Semiclassical Rabi models near multiphoton resonances in the presence of parametric modulation
• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Superradiant Phase Transition and Statistical Properties in the Dicke-Stark Model
• Detecting the Unruh Effect via an Engineered Low-Mass Field in a Superconducting Qubit
• Optimal control of a dissipative micromaser quantum battery in the ultrastrong coupling regime
• Single-photon scattering with counter rotating wave interaction
• Relative-belief inference in quantum information theory
• Dressed atom revisited: Hamiltonian-independent treatment of the radiative cascade
• Partial Decoherence and Thermalization through Time-Domain Ergodicity
• Solving the Jaynes-Cummings Model with Shift Operators Constructed by Means of the Matrix-Diagonalizing Technique
• Extraction of Work via a Thermalization Protocol
• Unconventional supersymmetric quantum mechanics in spin systems
• Many Electrons and the Photon Field -- The many-body structure of nonrelativistic quantum electrodynamics
• Renormalisation group flow of the Jaynes-Cummings model
• Parameter-dependent unitary transformation approach for quantum Rabi model
• Masked states of an atom coupled to a standing-wave cavity mode
• Two-Photon Scattering in USC regime
• Re-examining Einstein's $B$ coefficient and rate equations with the Rabi model
• Dynamical properties of the Rabi model
• Ultrastrong Coupling of a Qubit with a Nonlinear Optical Resonator
• Beyond the Rabi model: light interactions with polar atomic systems in a cavity
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery
• Metastability in the Dissipative Quantum Rabi Model
• Quantum phase transition of light in the dissipative Rabi-Hubbard lattice: A dressed-master-equation perspective
• Mean Field Theory for the Quantum Rabi Model, Inconsistency to the Rotating Wave Approximation
• Stabilization of product states and excited-state quantum phase transitions in a coupled qubit-field system
• Interference of cavity light by a single atom acting as a double slit
• A correspondence between the Rabi model and an Ising model with long-range interactions
• Eigenvalues and Eigenstates of Quantum Rabi Model
• Fast magnetic field manipulations and nonadiabatic geometric phases of nitrogen-vacancy center spin in diamond
• Controlling Symmetries and Quantum Criticality in the Anisotropic Coupled-Top Model
• An exactly solvable model for a strongly spin-orbit-coupled nanowire quantum dot
• Tunable anisotropic quantum Rabi model via a magnon--spin-qubit ensemble
• Heisenberg-Langevin Formalism For Open Circuit-QED Systems
• Quasi-integrability and nonlinear resonances in cold atoms under modulation
• A fast scheme for the implementation of the quantum Rabi model with trapped ions
• Analytically solvable model to the spin Hall effect with Rashba and Dresselhaus spin-orbit couplings
• Comment on `Parameter-dependent unitary transformation approach for quantum Rabi model'
• Probing the structure of entanglement with entanglement moments
• Photon-assisted Landau Zener transitions in a tunable driven Rabi dimer coupled to a micromechanical resonator
• Exact nonequilibrium hole dynamics, magnetic polarons and string excitations in antiferromagnetic Bethe lattices
• Approximate evolution for a system composed by two coupled Jaynes-Cummings Hamiltonians
• Energy cat states induced by a parity-breaking excited-state quantum phase transition
• Quantum heat transport in nonequilibrium anisotropic Dicke model
• Ladder of Loschmidt anomalies in the deep strong-coupling regime of a qubit-oscillator system
• Position-Resolved Resonance Quantization for Lossy Cavities
• Compact cavity-dressed Hamiltonian framework at arbitrarily strong light-matter coupling