Astrophysical observations indicate that there is roughly five times more dark matter in the Universe than ordinary baryonic matter, with an even larger amount of the Universes energy content due to dark energy. So far, the microscopic properties of these dark components have remained shrouded in mystery. In addition, even the five percent of ordinary matter in our Universe has yet to be understood, since the Standard Model of particle physics lacks any consistent explanation for the predominance of matter over antimatter. Inspired by these central problems of modern physics, we present here a direct search for interactions of antimatter with dark matter, and place direct constraints on the interaction of ultra-light axion-like particles $-$ one of the dark-matter candidates $-$ and antiprotons. If antiprotons exhibit a stronger coupling to these dark-matter particles than protons, such a CPT-odd coupling could provide a link between dark matter and the baryon asymmetry in the Universe. We analyse spin-flip resonance data acquired with a single antiproton in a Penning trap [Smorra et al., Nature 550, 371 (2017)] in the frequency domain to search for spin-precession effects from ultra-light axions with a characteristic frequency governed by the mass of the underlying particle. Our analysis constrains the axion-antiproton interaction parameter $f_a/C_{overline{p}}$ to values greater than $0.1$ to $0.6$ GeV in the mass range from $2 times 10^{-23}$ to $4 times 10^{-17},$eV/$c^2$, improving over astrophysical antiproton bounds by up to five orders of magnitude. In addition, we derive limits on six combinations of previously unconstrained Lorentz-violating and CPT-violating terms of the non-minimal Standard Model Extension.
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