Fig. presents the rate profile (blue), which is the same as the brown curve in panel b (with η c = 0.1), as well as the IR spectra calculated by HEOM (red). Details about the IR spectral calculation using HEOM are presented in Sec. I-D of the Supplementary Material. The IR spectra have a FWHM of about 60 cm -1 , and a peak position of ω c = ω 0 . The VSC modified rate profile has a FWHM of 140 cm -1 . The same peak position strongly indicates its common origin associated with the |ν L → |ν L transition. The optical transition is caused by -μ • E(t), where μ is the transition dipole operator, and E(t) is the classical laser field, whereas the moleculecavity coupling is caused by μ(â † + â) ∝ μ • qc , where qc = 1/(2ω c )(â † + â) is the photonic coordinate that is proportional to the displacement field inside the cavity.