inside the ĥB + ĤSB as the classical DOF, and we describe the polariton quantum subsystem in the diabatic basis of {|G, 1⟩ , |E n , 0⟩} for Ehrenfes dynamics, γ-SQC, spin-LSC, and spin-PLDM approaches. For the surface hopping method, the adiabatic polariton states and dark states (see Ref. 26) are required, which are defined as the eigenstates of Ĥpl = ĤS + ĤSB as follows