$Z_N$ symmetric chiral Rabi model: a new $N$-level system

Abstract

We present a new tractable quantum Rabi model for $N$-level atoms by extending the ${\mathbb{Z}}_2$ symmetry of the two-state Rabi model. The Hamiltonian is ${\mathbb{Z}}_N$ symmetric and allows the parameters in the level separation terms to be complex while remaining hermitian. This latter property means that the new model is {\em chiral}, which makes it differ from any existing $N$-state Rabi models in the literature. The ${\mathbb{Z}}_N$ symmetry provides partial diagonalization of the general Hamiltonian. The exact isolated (i.e. exceptional) energies of the model have the Rabi-like form but are $N$-fold degenerate. For the three-state case ($N=3$), we obtain three transcendental functions whose zeros give the regular (i.e. non-exceptional) energies of the model.

5 pages, no figures. This amended version states the differences between this model and the one in ref.[42], adds acknowledgements and some references, and corrects some misprints

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• The quantum Rabi model: solution and dynamics
• General phase spaces: from discrete variables to rotor and continuum limits
• Algebraic structure of the two-qubit quantum Rabi model and its solvability using Bogoliubov operators