Integrability vs exact solvability in the quantum Rabi and Dicke models

Abstract

The Rabi model describes the simplest interaction between light and matter via a two-level quantum system interacting with a bosonic field. We demonstrate that the fully quantised version of the Rabi model is integrable in the Yang-Baxter sense at two parameter values. The model is argued to be not Yang-Baxter integrable in general. This is in contrast to the claim that the quantum Rabi model is integrable based on a phenomenological criterion of quantum integrability not presupposing the existence of a set of commuting operators. Similar Yang-Baxter integrable points are identified for the generalised Rabi model and the fully quantised Dicke model. The integrable points have particular implications for the level statistics of the Dicke model.

5 pages, 1 figure, some points clarified, unified description of the Rabi and Dicke models, additional and updated references

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Cited by in corpus (6)

• The quantum Rabi model: solution and dynamics
• Approximated integrability of the Dicke model
• The asymmetric quantum Rabi model in the polaron picture
• Asymptotic behavior of observables in the asymmetric quantum Rabi model
• An analytical variational method for the biased quantum Rabi model in the ultra-strong coupling regime
• A transition in the spectral statistics of quantum optical model by different electromagnetic fields