We use the Holstein-Tavis-Cummings (HTC) Hamiltonian to model the polariton dy-namics in the collective coupling regime. The total Hamiltonian can be separated into a component describing the system term ĤS , a component describing the bath term ĥB , and a system-bath interaction term ĤSB . This separation of terms is expressed as ĤHTC = ĤS + ĥB + ĤSB .