Fig. presents the infrared (IR) profile of the RPV mode (red curve), alongside the cavity-dependent rate profile (blue curve) obtained from the HEOM simulations (blue dots) and the FGR approach (blue solid line) outlined in Eq. 8. Both profiles exhibit a distinct sharp peak around ω Q , which is an essential feature observed in most VSC experiments . In particular, existing theories for resonance suppression often have a much broader rate of constant peak (as a function of cavity frequency) that is significantly broader than the width of the lineshape . To the best of our knowledge, Eq. 16 is the first analytic theory that is capable of describing a sharp resonance suppression behavior indicated in Fig. .