ZN symmetric chiral Rabi model: A new N-level system

We present a new tractable quantum Rabi model for N-level atoms by extending the Z(2) symmetry of the two-state Rabi model. The Hamiltonian is 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 chiral, which makes it differ from any existing N-state Rabi models in the literature. The 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. (c) 2014 Elsevier Inc. All rights reserved.