We use Drude-Lorentz model spectral density, with γ 0 = 200 cm -1 , γ Q = 6000 cm -1 for the bath characteristic frequencies and λ 0 = 83.6 cm -1 , λ Q = 0.147 cm -1 for the reorganization energies, similar to the previous work . Finally, the cavity mode interacts with the outside cavity electromagnetic field that acts as a bath for the cavity mode, thus describing the cavity loss Ĥloss = 1 2 υ pυ + ω 2 υ xυ -