My teacher told me to calculate atom-photon interaction with QFT. But all textbooks talk about elementary particles only. Lewenstein et al. studied QFT of atoms and photons, but he started from the Hamiltonian.
Yes, but it's hard, due to the variety of interactions that can happen between the photon and the internal structure of the atom.
An easier example that you might find interesting and that is covered in many textbooks is deep inelastic scattering. Typically, it's the interaction of an electron with a proton (which is also the hydrogen nucleus) through photon exchange.
The gist of it is, it's horribly complicated to study in detail, so as far as I know it's usually done by introducing a form factor, which is more or less an effective, renormalized, wavefunction for the proton. Its value is predicted by various models, depending on the energy, with experimental input.
In practice, as soon as you have strong interaction somewhere in a system, things get complicated quicky, and you usually fall back to effective models like this one.