which can be intuitively understood as the dipole fluctuations due to coupling to the cavity. The variational expectation value in Eq. 123 suggests that the eigenstates of this Hamiltonian are simply the Fock states. However, one should not be confused by its appearance as HF needs to be solved through many iterations (in a self-consistent manner), and for each iteration, the shift Z needs to be re-evaluated, and a new unitary transformation needs to be constructed, similar to how the HF density matrix needs to be reconstructed to progress the self-consistent cycle.