Quantifying the rotating-wave approximation of the Dicke model

• URL: http://arxiv.org/abs/2410.18694v1
• Date: Thu, 24 Oct 2024 12:43:09 GMT
• Title: Quantifying the rotating-wave approximation of the Dicke model
• Authors: Leonhard Richter, Daniel Burgarth, Davide Lonigro,
• Abstract summary: 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. Our bounds are intrinsically state-dependent and, in particular, are significantly different in the cases of entangled and non-entangled states.
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• Abstract: 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, are significantly different in the cases of entangled and non-entangled states; this behaviour also seems to be confirmed by the numerics.

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