  We present a theoretical investigation of the expected experimental signals
produced by freely falling atoms with time oscillating mass and transition
frequency. These oscillations could be produced in a variety of models, in
particular, models of scalar dark matter (DM) non universally coupled to the
standard matter (SM) such as axion-like particles (ALP) and dilatons.
Performing complete and rigorous calculations, we show that, on one hand, two
different atomic species would accelerate at a different rate, and on the other
hand, they would produce a non-zero differential phase shift in atom
interferometers (AI). The former would produce observable signals in
equivalence principle tests like the recent MICROSCOPE mission, and we provide
a corresponding sensitivity estimate, showing that MICROSCOPE can reach beyond
the best existing searches in the ALP case. We also compare the expected
sensitivity of two future AI experiments, namely the AION-10 gradiometer and an
isotope differential AI considered for MAGIS-100, that we will refer to as
SPID. We show that the SPID setup would be more sensitive to these dark matter
fields compared to the gradiometer one, assuming equivalent experimental
parameters.
