A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| author | Kafuri, A. Maldonado-Villamizar, F. H. Moroz, A. Rodríguez-Lara, B. M. |
| author_facet | Kafuri, A. Maldonado-Villamizar, F. H. Moroz, A. Rodríguez-Lara, B. M. |
| contents | 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 $u(1 \vert 1)$ 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 $osp(2 \vert 2)$ 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 Lie theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model Kafuri, A. Maldonado-Villamizar, F. H. Moroz, A. Rodríguez-Lara, B. M. Quantum Physics 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 $u(1 \vert 1)$ 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 $osp(2 \vert 2)$ 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 Lie theory. |
| title | A supersymmetry journey from the Jaynes-Cummings to the anisotropic Rabi model |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2402.17881 |