You have attempted to access the full-text of an Early Posting article. Access is available via an institutional subscription.
See the Early Posting FAQ page for additional information.
See the Early Posting FAQ page for additional information.
A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
JOSA B- received 02/29/2024; accepted 04/24/2024; posted 04/24/2024; Doc. ID 522504
- Abstract: We revisit the Jaynes--Cummings and anti-Jaynes--Cummings model through the lens of the Lie theory, aiming to highlight the efficacy of operator-based approach for an explicit diagonalization.We focus on explicitly delineating the steps to go from an underlying abstract supersymmetry, provided by the $u(1 \vert 1)$ 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 $ops(2 \vert 2)$ 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 the Lie theory.