where ρ is the reduced density operator of the quantum subsystem including the electronic and photonic DOFs, Ĥ is the polaritonic Hamiltonian including the non-adiabatic terms, L is a Lindblad jump operator that mediates the dissipation due to an effective environment (i.e., loss channel), Γ is the dissipation rate, { Â, B } = Â B + B Â is the anticommutator of matrices Â and B and [ Â, B ] = Â B -B Â is the commutator. L Coh. and L Diss. are super-operators in Liouville space which describe the quantum mechanical evolution of the electron-photon subsystem under the Hermitian Hamiltonian Ĥ which governs the coherent evolution of the system and L which governs the dissipation (i.e., incoherent evolution). Lindblad dynamics ensure the conservation of the total population of the system. The Lindblad jump operator that governs the photon dissipation channel in Fabry-Perot cavities is defined as,