Dear Colleagues,

Prototypical quantum optics models, such as for example the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models, are commonly analyzed with diverse techniques, including analytical exact solutions, mean-field theory, exact diagonalization, and the like. The analysis of these systems strongly depends on their symmetries, ranging, e.g., from a U(1) group in the Jaynes–Cummings model to a Z₂ symmetry in the full-fledged quantum Rabi model.

In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deep-strong coupling regimes, have been attracting an increasing amount of interest. The quantum Rabi and Dicke models in these exotic regimes present new features, such as collapses and revivals of the population, bounces of photon-number wave packets, as well as the breakdown of the rotating-wave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few- or many-qubit systems considered have associated inhomogeneous or equal couplings to the bosonic mode.

Moreover, there is a growing interest in proposing and carrying out quantum simulations of these models in quantum platforms such as, e.g., trapped ions, superconducting circuits, and quantum photonics.

In this Special Issue, we intend to gather a series of articles related to symmetry in quantum optics models, possibly including, but not exclusively, the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models. We will also consider their generalizations to, e.g., inhomogeneous light–matter couplings, bias terms, time-dependent couplings, as well as all possible regimes of the light–matter interaction. We welcome papers on mathematical physics, related either to spectral analysis or time dynamics, as well as more applied articles with proposals for implementations of and/or experiments with these or related models in quantum platforms, such as trapped ions, superconducting circuits, and quantum photonics.

Prof. Dr. Lucas Lamata
Guest Editor

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• Quantum Rabi model
• Dicke model
• Mathematical physics
• Quantum simulations
• Trapped ions
• Superconducting circuits
• Quantum photonics
• Ultrastrong light–matter coupling regime