  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 Universe's 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.

Atomic Physics;Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology