Because this NH-CQED-CIS Hamiltonian is non-Hermitian, the left and right eigenvectors, which we will denote Ψ L I and Ψ R I for the left and right eigenvectors for the NH-CQED-CIS state I respectively, are not simply complex conjugates of each other. However, the left and right eigenvectors can be chosen to be biorthogonal, where biorthogonality implies 45