The bath is assumed to be in thermal equilibrium, where Z b = Tr[e -β Ĥb ] is the partition function, with β = 1/k B T and we consider T = 300 K throughout this work. To compare the decoherence dynamics outside the cavity, we take the g c = 0 + limit, such that the mixing angle lim gc→0 + Θ N = π/4 under the resonant condition (see Eq. 12). Thus, the initial condition |Ψ(0)⟩ for the outside cavity case can still be interpreted in Eq. 19, and under the g c = 0 + limit one still have well-defined states