Fig. presents J eff (ω) under different cavity lifetimes, where we fix ω c = ω 0 = 1172 cm -1 . One can observe that J eff (ω) exhibits a sharp peak when there is a relatively long τ c . It will reduce to a Dirac δ-function at the lossless limit (τ c → ∞), whose bare-bath TCF is discussed in Sec. I-B of the Supplementary Material. Decreasing Note that the cavity modification effects become smaller when τc is reduced, and the cavity effect vanishes under the heavy loss limit (τc → 0). (c) The peak value of k/k0 (at ωc = ω0) as a function of cavity lifetime τc.