A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
arXiv:2402.17881 · doi:10.1364/JOSAB.522504
Abstract
We revisit the Jaynes-Cummings and anti-Jaynes-Cummings model through the lens of Lie theory, aiming to highlight the efficacy of an operator-based approach for diagonalization. We focus on explicitly delineating the steps from an underlying abstract supersymmetry, provided by the superalgebra, into concrete proper states and energies in the laboratory frame. Additionally, we explore the anisotropic Rabi model possessing an underlying supersymmetry, provided by the superalgebra, in a squeezed reference frame, where it is possible to approximate its spectral characteristics by an effective Jaynes--Cummings model. Finally, we identify a regime for a factorizable anisotropic Rabi model, exhibiting an equally spaced, double degenerate energy spectrum with a unique ground state energy. Our work aims to merge mathematical physics with practical quantum optics, underscoring the critical role of Lie theory.
21 pages, 4 figures
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