Integrability of the Rabi model.

By D. Braak. Physical Review Letters, 2011

632 citations recorded by the source corpus.

The Rabi model is a paradigm for interacting quantum systems. It couples a bosonic mode to the smallest possible quantum model, a two-level system. I present the analytical solution which allows us to consider the question of integrability for quantum systems that do not possess a classical limit. A criterion for quantum integrability is proposed which shows that the Rabi model is integrable due to the presence of a discrete symmetry. Moreover, I introduce a generalization with no symmetries; the generalized Rabi model is the first example of a nonintegrable but exactly solvable system.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/442e15682df888cfed6f492dc795f38d8cab6591

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons (2012, background): “However, when ωr ∝ g then the counter rotating terms cannot be ignored, and H takes the form of the Rabi model hamiltonian [13].”
Circuit QED: Superconducting Qubits Coupled to Microwave Photons (2015, methodology): “If we had not made the RWA, we would have the so-called Rabi Hamiltonian which in a certain sense is also integrable(Braak, 2011).”
Multiphoton quantum Rabi oscillations in ultrastrong cavity QED (2015, background): “Moreover, for θ = 0 parity is conserved [46,47] and only states with an even number of excitations contribute to |0〉.”
Microwave photonics with superconducting quantum circuits (2017, background): “It was only a few years ago that an analytical solution was finally found, given in the form of transcendental functions [418,419].”
Quantum Simulation Of The Quantum Rabi Model In A Trapped Ion (2017, background): “Regardless of the apparent simplicity of its succint Hamiltonian form, an analytical solution of the QRM has only recently been found [22].”
Semi-classical and quantum Rabi models: in celebration of 80 years (2016, methodology): “There are three basic reasons: (i) experiments have now been able to push into the ultrastrong (|ω| < 10g) [4, 5] and deep strong (|ω| < g) [6] coupling regimes in which the rotating-wave approximation and thus the Jaynes-Cummings model are not applicable; (ii) there are exciting prospects for novel”