Quantifying the rotating-wave approximation of the Dicke model
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866914309364252672 |
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| author | Richter, Leonhard Burgarth, Daniel Lonigro, Davide |
| author_facet | Richter, Leonhard Burgarth, Daniel Lonigro, Davide |
| contents | We analytically find quantitative, non-perturbative bounds to the validity of the rotating-wave approximation (RWA) for the multi-atom generalization of the quantum Rabi model: the Dicke model. Precisely, we bound the norm of the difference between the evolutions of states generated by the Dicke model and its rotating-wave approximated counterpart, that is, the Tavis-Cummings model. The intricate role of the parameters of the model in determining the bounds is discussed and compared with numerical results. Our bounds are intrinsically state-dependent and, in particular, capture a nontrivial dependence on the total angular momentum of the initial state; this behaviour also seems to be confirmed by accompanying numerical results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_18694 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantifying the rotating-wave approximation of the Dicke model Richter, Leonhard Burgarth, Daniel Lonigro, Davide Quantum Physics Mathematical Physics We analytically find quantitative, non-perturbative bounds to the validity of the rotating-wave approximation (RWA) for the multi-atom generalization of the quantum Rabi model: the Dicke model. Precisely, we bound the norm of the difference between the evolutions of states generated by the Dicke model and its rotating-wave approximated counterpart, that is, the Tavis-Cummings model. The intricate role of the parameters of the model in determining the bounds is discussed and compared with numerical results. Our bounds are intrinsically state-dependent and, in particular, capture a nontrivial dependence on the total angular momentum of the initial state; this behaviour also seems to be confirmed by accompanying numerical results. |
| title | Quantifying the rotating-wave approximation of the Dicke model |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2410.18694 |