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We revisit the interaction of a first-quantized atomic system (consisting oftwo charged quantum particles) with the quantum electromagnetic field, pointingout the subtleties related to the gauge nature of electromagnetism and theeffect of multipole approximations. We connect the full minimal-coupling modelwith the typical effective models used in quantum optics and relativisticquantum information such as the Unruh-DeWitt (UDW) model and the dipolecoupling approximation. We point out in what regimes different degrees ofapproximation are reasonable and in what cases effective models need to berefined to capture the features of the light-matter interaction. This isparticularly important when considering the center of mass (COM) of the atom asa quantum system that can be delocalized over multiple trajectories. Forexample, we show that the simplest UDW approximation with a quantum COM failsto capture crucial R\"ontgen terms coupling COM and internal atomic degrees offreedom with each other and the field. Finally we show how effective dipoleinteraction models can be covariantly prescribed for relativistically movingatoms.

Quantum delocalization, gauge and quantum optics: The light-matter interaction in relativistic quantum information