  We propose the nuclear interferometer - a single-photon interferometry
experiment based upon the thorium-229 nuclear clock transition - as a novel
detector for ultra-light dark matter (ULDM). Thanks to the enhanced sensitivity
of this transition to the variation of fundamental constants, we find that
possible realisations of such an experiment deploying either single ions or
clouds of atoms have the potential to be complementary to advanced
very-long-baseline terrestrial clock atom interferometers in the search for
ultra-light dark matter with scalar couplings to photons. Nuclear
interferometry may also offer an unparalleled window to new physics coupling to
the QCD sector via quarks or gluons, with a discovery reach that could enhance
existing and proposed experiments over a range of frequencies in the direction
of well-motivated parameter space.
