We show that the Hamiltonian describing $N$ nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge $Z$, has a ground state when $N$ is less than $Z+1$. The result holds for any value of the fine structure constant $\alpha$ and for any value of the ultraviolet cutoff $\Lambda$ on the radiation field. There is no infrared cutoff. The basic mathematical ingredient in our proof is a novel localization of the electromagnetic field in such a way that the errors in the energy are of smaller order than $1/L$, where $L$ is the localization radius.
"Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics." Adv. Theor. Math. Phys. 7 (4) 667 - 710, July 2003.