  Atom interferometers with long baselines are envisioned to complement the
ongoing search for dark matter. They rely on atomic manipulation based on
internal (clock) transitions or state-preserving atomic diffraction.
Principally, dark matter can act on the internal as well as the external
degrees of freedom to both of which atom interferometers are susceptible. We
therefore study in this contribution the effects of dark matter on the internal
atomic structure and the atoms' motion. In particular, we show that the atomic
transition frequency depends on the mean coupling and the differential coupling
of the involved states to dark matter, scaling with the unperturbed atomic
transition frequency and the Compton frequency, respectively. The differential
coupling is only of relevance when internal states change, which makes
detectors, e.g., based on single-photon transitions sensitive to both coupling
parameters. For sensors generated by state-preserving diffraction mechanisms
like Bragg diffraction, the mean coupling modifies only the motion of the atom
as the dominant contribution. Finally, we compare both effects observed in
terrestrial dark-matter detectors.
