The quantum Rabi model: solution and dynamics

Abstract

This article presents a review of recent developments on various aspects of the quantum Rabi model. Particular emphasis is given on the exact analytic solution obtained in terms of confluent Heun functions. The analytic solutions for various generalisations of the quantum Rabi model are also discussed. Results are also reviewed on the level statistics and the dynamics of the quantum Rabi model. The article concludes with an introductory overview of several experimental realisations of the quantum Rabi model. An outlook towards future developments is also given.

42 pages, 13 figures. Minor changes, references added

References in corpus (96)

• Cavity Optomechanics
• Cavity quantum electrodynamics for superconducting electrical circuits: an architecture for quantum computation
• Quantum state engineering with Josephson-junction devices
• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• On the Integrability of the Rabi Model
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• Natural and artificial atoms for quantum computation
• Superconducting qubit-oscillator circuit beyond the ultrastrong-coupling regime
• Quantum jumps of light recording the birth and death of a photon in a cavity
• Deep Strong Coupling Regime of the Jaynes-Cummings model
• Climbing the Jaynes-Cummings Ladder and Observing its Sqrt(n) Nonlinearity in a Cavity QED System
• Progressive field-state collapse and quantum non-demolition photon counting
• Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime
• Quantum Phase Transition and Universal Dynamics in the Rabi model
• Generalized rotating-wave approximation for arbitrarily large coupling
• Hybrid circuit cavity quantum electrodynamics with a micromechanical resonator
• Exact solvability of the quantum Rabi models within Bogoliubov operators
• Ultrastrong coupling regime of cavity QED with phase-biased flux qubits
• Quantum electrodynamics near a photonic band-gap
• Vacuum Rabi oscillations in a macroscopic superconducting qubit LC oscillator system
• Ultrafast Quantum Gates in Circuit QED
• Quantum Measurement of a Coupled Nanomechanical Resonator -- Cooper-Pair Box System
• A Single Photon Can Simultaneously Excite Two or More Atoms
• Quantum Rabi Model with Trapped Ions
• Strong Coupling of a Quantum Oscillator to a Flux Qubit at its Symmetry Point
• Multiphoton Quantum Rabi Oscillations in Ultrastrong Cavity QED
• Photonic realization of the quantum Rabi model
• Semi-classical and quantum Rabi models: in celebration of 80 years
• Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
• Spectral collapse via two-phonon interactions in trapped ions
• Quasi-Exactly Solvable Systems and Orthogonal Polynomials
• Analytical eigenstates for the quantum Rabi model
• Anisotropic Rabi model
• Two-photon Rabi model: Analytic solutions and spectral collapse
• Exact Solvability of the two-photon Rabi Hamiltonian
• Stark effect and generalized Bloch-Siegert shift in a strongly driven two-level system
• Two-photon lasing by a single quantum dot in a high-Q microcavity
• Full spectrum of the Rabi model
• Yang-Baxter integrable models in experiments: from condensed matter to ultracold atoms
• Analytical solutions for the Rabi model
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Ground-state phase diagram of the quantum Rabi model
• Absence of Vacuum Induced Berry Phases without the Rotating Wave Approximation in Cavity QED
• Analytical method of spectra calculations in the Bargmann representation
• Exact real-time dynamics of the quantum Rabi model
• Bloch-Siegert shift of the Rabi model
• Integrability vs Quantum Thermalization
• Effects of counterrotating interaction on driven tunneling dynamics: coherent destruction of tunneling and Bloch-Siegert shift
• Solution of the Dicke model for N=3
• Exact isolated solutions for the two-photon Rabi Hamiltonian
• On the solvability of the quantum Rabi model and its 2-photon and two-mode generalizations
• Symmetric Rotating Wave Approximation for the Generalized Single-Mode Spin-Boson System
• An exactly solvable system from quantum optics
• Dynamical correlation functions and the quantum Rabi model
• Quantum Rabi model for N-state atoms
• Exceptional and regular spectra of a generalized Rabi model
• Bogoliubov transformations and exact isolated solutions for simple non-adiabatic Hamiltonians
• On solvability and integrability of the Rabi model
• Quantum Dynamics of the Driven and Dissipative Rabi Model
• Note on the Analytical Solution of the Rabi Model
• Continued Fractions and the Rabi Model
• Generalized rotating-wave approximation to the two-qubit and cavity coupling system
• Solution of the two-mode quantum Rabi model using extended squeezed states
• Analytical ground state for the Jaynes-Cummings model with the ultrastrong coupling
• A hidden analytic structure of the Rabi model
• Oscillator tunneling dynamics in the Rabi model
• Comment on "Solvability of the two-photon Rabi Hamiltonian"
• On the spectrum of a class of quantum models
• Generalized rotating-wave approximation to biased qubit-oscillator systems
• Solutions to the quantum Rabi model with two equivalent qubits
• Exceptional solutions in two-mode quantum Rabi models
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• Quantum state engineering in hybrid open quantum systems
• Analytical Solution for the Anisotropic Rabi Model: Effects of Counter-Rotating Terms
• Quadratic Lie algebras and quasi-exact solvability of the two-photon Rabi Hamiltonian
• Absence of collapse in quantum Rabi oscillations
• Generalized Rabi models: diagonalization in the spin subspace and differential operators of Dunkl type
• Charge transfer and coherence dynamics of tunnelling system coupled to a harmonic oscillator
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• Entanglement dynamics of the ultra-strong coupling three-qubit Dicke model
• Quantum integrability and nonintegrability in the spin-boson model
• Dissipative two-level systems under ultrastrong off-resonant driving
• The vacuum induced Berry phase beyond rotating-wave approximation
• $Z_N$ symmetric chiral Rabi model: a new $N$-level system
• Does the Berry phase in a quantum optical system originate from the rotating wave approximation
• Analytical solutions and genuine multipartite entanglement of the three-qubit Dicke model
• The asymmetric quantum Rabi model in the polaron picture
• Ground state of the asymmetric Rabi model in the ultrastrong coupling regime
• Physical background for parameters of the quantum Rabi model
• Quasi-exactly solvable models based on special functions
• Continued fraction solution to the Raman interaction of a trapped ultracold ion with two traveling wave lasers
• Quantum models with spectrum generated by the flows of polynomial zeros
• Geometric Curvature and Phase of the Rabi model
• A Parafermionic Generalization of the Jaynes Cummings Model
• Exact analysis of the spectral properties of the anisotropic two-bosons Rabi model

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• Simple scheme for extracting work with a single bath
• Thermodynamic Limit in the Two-qubit Quantum Rabi Model with Spin-Spin Coupling
• Ground State Excitation of an Atom Strongly Coupled to a Free Quantum Field
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• Spectral Signatures of Vibronic Coupling in Trapped Cold Ionic Rydberg Systems
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• $\mathcal{P}\mathcal{T}$-symmetric quantum Rabi model: Solutions and exceptional points
• Cavity quantum electrodynamics of photonic temporal crystals
• Two-photon sideband transition in a driven quantum Rabi model : Quantitative discussions with derived longitudinal drives and beyond the rotating wave approximation
• Quantum thermalization and thermal entanglement in the open quantum Rabi model
• Rabi oscillations, entanglement and teleportation in the anti-Jaynes-Cummings model
• Controlling qubit-oscillator systems using linear parameter sweeps
• The Unruh-DeWitt model and its joint interacting Hilbert space
• Floquet analysis of extended Rabi models based on high-frequency expansion
• Quantum criticality driven by the cavity coupling in Rabi-dimer model
• Quantum-Electrodynamical Density-Functional Theory Exemplified by the Quantum Rabi Model
• Defining a well-ordered Floquet basis by the average energy
• Analytical solution of the open dispersive Jaynes-Cummings model and perturbative analytical solution of the open quantum Rabi model
• Thermalization of open quantum systems using the multiple-Davydov-D2 variational approach
• Critical Quantum Sensing: a tutorial on parameter estimation near quantum phase transitions
• Quantum aspects of spacetime: A quantum optics view of acceleration radiation and black holes
• Quantum sensing with ultracold simulators in lattice and ensemble systems: a review
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• Effective description of cooling and thermal shifts in quantum systems coupled to bosonic modes
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• Photon pumping, photodissociation and dissipation at interplay for the fluorescence of a molecule in a cavity
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• Low-temperature Quantum Metrology Enhanced by Strong Couplings
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• $\mathcal{P}\mathcal{T}$-symmetric two-photon quantum Rabi models
• Bounding the rotating wave approximation for coupled harmonic oscillators
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• Ultrastrong Coupling of a Qubit with a Nonlinear Optical Resonator
• Error Bounds for Open Quantum Systems with Harmonic Bosonic Bath
• Comparison of Quantum and Semiclassical Rabi models near multiphoton resonances in the presence of parametric modulation
• Spin Phonon Relaxation Dynamics from a Conical Intersection of Trapped Rydberg Ions
• Dressed atom revisited: Hamiltonian-independent treatment of the radiative cascade
• Generalization of the Einstein coefficients and rate equations under the quantum Rabi oscillation
• Evanescent Wave Approximation for Non-Hermitian Hamiltonians
• Dynamical properties of the Rabi model
• Unconventional supersymmetric quantum mechanics in spin systems
• Nutation dynamics and multifrequency resonance in a many-body seesaw
• Eigenvalues and Eigenstates of Quantum Rabi Model
• Tunable anisotropic quantum Rabi model via a magnon--spin-qubit ensemble
• Comment on `Parameter-dependent unitary transformation approach for quantum Rabi model'
• Stokes graphs of the Rabi problem with real parameters
• Long-time signatures of chaos in large atom-light frequency ratios Rabi model
• Beyond the Rabi model: light interactions with polar atomic systems in a cavity
• Topological enhancement of a PT-symmetric Su-Schrieffer-Heeger quantum battery
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