  Axion-gluon interaction induces quadratic couplings between the axion and the
matter fields. We find that, if the axion is an ultralight dark matter field,
it induces small oscillations of the mass of the hadrons as well as other
nuclear quantities. As a result, atomic energy levels oscillate. We use
currently available atomic spectroscopy data to constrain such axion-gluon
coupling. We also project the sensitivities of future experiments, such as ones
using molecular and nuclear clock transitions. We show that current and
near-future experiments constrain a finely-tuned parameter space of axion
models. These can compete with or dominate the already-existing constraints
from oscillating neutron electric dipole moment and supernova bound, in
addition to those expected from near future magnetometer-based experiments. We
also briefly discuss the reach of accelerometers and interferometers.
