Fig. 5: Observables of the Renormalized QRM.
From: Renormalization and low-energy effective models in cavity and circuit quantum electrodynamics
a Expectation value of \({(\hat{a}+{\hat{a}}^{{\dagger} })}^{2}\) (a) on the third excited state of the full model (blue solid), QRM (red dashed) and the RQRM (green dash-dotted), as a function of the coupling strength g/ωc. The RQRM provides more accurate results, even for strong coupling strengths. Matrix elements of the cavity field \(\hat{a}+{\hat{a}}^{{\dagger} }\) (b) and the atomic position operator \(\hat{x}\) (c) between the ground and the second excited, as a function of g/ωc. While in the panel (b) the renormalization improves the accuracy, in the panel c it does not. This behavior can be explained by the infidelity of the second excited state of the RQRM with respect to the QRM, as a function of g/ωc, for both the reduced density matrix of the cavity (solid light blue) and the atom (dashed orange) (d).
