where Tn represents the nuclear kinetic energy operator, Ĥen is the electronic Hamiltonian that describes electron-nucleus interactions. Further, Ĥp , Ĥenp , and Ĥd represent the photonic Hamiltonian, electronic-nuclearphotonic interactions, and the DSE, respectively. A full derivation of this Hamiltonian, as well as its connection with the various atomic cavity QED models can be found in the Appendix of Ref. 33.