It should be noted that this expression uses the notation from Ref. 53. These eigenstates should not be confused with the Jaynes-Cummings (JC) eigenstates (see Eq. 50) which are the exact eigenvectors of the JC Hamiltonian (see Eq. 49). In the deep strong coupling limit, the overlap between the PFS n -|n + -→ 0. In this case, one can clearly see that the eigenstates |Ψ ±,n become doubly degenerate with E +,n = E -,n and the MH diabatic states |µ ± , n are the eigenstates of the light-matter Hamiltonian where the corresponding eigenenergies simplify to the energies of these MH states added to the energy of n photons.