shown in Fig. (left panel) exhibits resonant dynamical localization for ω min c ≈ 1300 cm -1 . Note that the ⟨P iso ⟩ in Fig. ) also shows maximum suppression around the same value of the cavity frequency. Moreover, ⟨q⟩(η, ω c ) is the measure used earlier to map the localization landscape. Although not shown here, our computations show that essentially the same correlation with the classical phase space features is observed for other initial states and for different parameters of the reactive mode potential. In supplementary Sec. S3 we show the results for the case of a deeper double well potential.