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 (30)

• Beyond the Jaynes-Cummings model: circuit QED in the ultrastrong coupling regime
• Observation of the Bloch-Siegert Shift in a Qubit-Oscillator System in the Ultrastrong Coupling Regime
• 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
• Generalized rotating-wave approximation for arbitrarily large coupling
• Ultrastrong coupling regime of cavity QED with phase-biased flux qubits
• Strong Coupling of a Quantum Oscillator to a Flux Qubit at its Symmetry Point
• Integrability vs exact solvability in the quantum Rabi and Dicke models
• Analytical method of spectra calculations in the Bargmann representation
• Exact real-time dynamics of the quantum Rabi model
• An exactly solvable system from quantum optics
• Dynamical correlation functions and the quantum 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
• On the spectrum of a class of quantum models
• Concise analytic solutions to the quantum Rabi model with two arbitrary qubits
• 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
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators
• Exact solvability, non-integrability, and genuine multipartite entanglement dynamics of the Dicke model
• Quantum integrability and nonintegrability in the spin-boson model
• Charge transfer and coherence dynamics of tunnelling system coupled to a harmonic oscillator
• $Z_N$ symmetric chiral Rabi model: a new $N$-level system
• The asymmetric quantum Rabi model in the polaron picture
• Does the Berry phase in a quantum optical system originate from the rotating wave approximation
• Quasi-exactly solvable models based on special functions
• A Parafermionic Generalization of the Jaynes Cummings Model