and the photon-loss bath spectral density is J c (ω) ≡ (π/2) j (c 2 j /ω j )δ(ω -ωj ) = (ω/τ c ) exp(-ω/ω m ), where τ c is the cavity lifetime , and we had assumed that photon loss satisfies strict Ohmic dissipation. In other words, as the cutoff frequency ω m → ∞, the photon bath dynamics reach the Markovian limit . By performing a normal mode transformation, one can obtain a simple system-bath model that is described by an effective spectral density (which is of the Brownian oscillator form ). Details are provided in Supplementary Note 2, section A.