  We revisit the interaction of a first-quantized atomic system (consisting of
two charged quantum particles) with the quantum electromagnetic field, pointing
out the subtleties related to the gauge nature of electromagnetism and the
effect of multipole approximations. We connect the full minimal-coupling model
with the typical effective models used in quantum optics and relativistic
quantum information such as the Unruh-DeWitt (UDW) model and the dipole
coupling approximation. We point out in what regimes different degrees of
approximation are reasonable and in what cases effective models need to be
refined to capture the features of the light-matter interaction. This is
particularly important when considering the center of mass (COM) of the atom as
a quantum system that can be delocalized over multiple trajectories. For
example, we show that the simplest UDW approximation with a quantum COM fails
to capture crucial R\"ontgen terms coupling COM and internal atomic degrees of
freedom with each other and the field. Finally we show how effective dipole
interaction models can be covariantly prescribed for relativistically moving
atoms.
