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

2014/03/21 by Yao-Zhong Zhang · 1 citation
Physics and Astronomy · Mathematics · #quant-ph #cond-mat.other #math-ph #math.MP

paper · pdf · doi:10.1016/j.aop.2014.05.003

published as Ann. Phys. (N.Y.) 347 (2014), 122-129 · 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

arxiv created 2014/03/21 · arxiv updated 2014/05/23

Abstract

We present a new tractable quantum Rabi model for N-level atoms by extending the \mathbb Z₂ 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.

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