is the Bose-Einstein distribution function, β = 1/(k B T ) is the inverse temperature, and k B is the Boltzmann constant. Further, Γ c is the photon-loss rate, { Â, B} = Â B + B Â denotes the anti-commutator. The quantum dynamics of Hamiltonian in Eq. 1 with the Lindblad dissipators are simulated using mixed HEOM-Lindblad formalism , described in Sec. V A.