The diabatic polaritonic Hamiltonian (also known as the Tavis-Cummings Hamiltonian 67 ) is the system Hamiltonian Ĥpl = Ĥ -( Ĥb + Ĥsb ), whose eigenstates are two bright polariton states and N -1 dark states (with zero transition dipole from the overall ground state |G⟩ ⊗ |0⟩). In the single exciton basis, the Upper polariton state (UP or |+⟩) and Lower polariton state (LP or |-⟩) are superpositions of the bright exciton state (|B⟩ = B † |G⟩), expressed as