One such basis that provides computational as well as conceptual convenience is the recently proposed polarized Fock State (PFS) basis introduced in Ref. 41. Here, the Pauli-Fierz Hamiltonian (Eq. 109) is rewritten using an entangled electronic-photonic basis, where matter is represented in the eigenstates of the dipole operator ν P μ P = µ νν (R)|ϕ ν ⟩⟨ϕ ν | and is referred to as the Mulliken-Hush (MH) representation (see details around Eq. 29). The light-matter Hamiltonian (see Eq. 109) using the MH basis can be written as,