Quantifying the rotating-wave approximation of the Dicke model

TL;DR

This paper provides analytical, non-perturbative bounds on the validity of the rotating-wave approximation in the Dicke model, considering state-dependent factors and initial total angular momentum.

Contribution

It introduces a novel, quantitative method to bound the difference between the Dicke model and its RWA approximation, accounting for state and parameter dependencies.

Findings

Bounds are state-dependent and incorporate total angular momentum effects.

Numerical results support the analytical bounds.

The role of model parameters in the RWA validity is clarified.

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, capture a nontrivial dependence on the total angular momentum of the initial state; this behaviour also seems to be confirmed by accompanying numerical results.