is the Bose-Einstein distribution function, where β ≡ 1/(k B T ) is the inverse of temperature T , k B is the Boltzmann constant. In typical VSC experiments , ω 0 ≈ 1200 cm -1 and room temperature 1/β = k B T ≈ 200 cm -1 , such that βℏω 0 ≫ 1 and n(ω) can be approximate as Boltzmann distribution. Under the lossy regime (τ c ≪ Ω -1 R ), Eq. 2 agrees well with the numerically exact HEOM results, and has a sharp peak at