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Symmetries in the Quantum Rabi Model

Max-Planck Institute for Solid State Research, Heisenbergstr. 1, 70569 Stuttgart, Germany
Symmetry 2019, 11(10), 1259; https://doi.org/10.3390/sym11101259
Received: 21 September 2019 / Revised: 5 October 2019 / Accepted: 6 October 2019 / Published: 9 October 2019
(This article belongs to the Special Issue Symmetry in Quantum Optics Models)
The quantum Rabi model is the simplest and most important theoretical description of light–matter interaction for all experimentally accessible coupling regimes. It can be solved exactly and is even integrable due to a discrete symmetry, the Z 2 or parity symmetry. All qualitative properties of its spectrum, especially the differences to the Jaynes–Cummings model, which possesses a larger, continuous symmetry, can be understood in terms of the so-called “G-functions” whose zeroes yield the exact eigenvalues of the Rabi Hamiltonian. The special type of integrability appearing in systems with discrete degrees of freedom is responsible for the absence of Poissonian level statistics in the spectrum while its well-known “Juddian” solutions are a natural consequence of the structure of the G-functions. The poles of these functions are known in closed form, which allows drawing conclusions about the global spectrum. View Full-Text
Keywords: light–matter interaction; integrable systems; global spectrum light–matter interaction; integrable systems; global spectrum
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Braak, D. Symmetries in the Quantum Rabi Model. Symmetry 2019, 11, 1259.

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