The striking imbalance of matter and antimatter in our universe is one of the hottest topics of modern physics, which inspires experiments to compare the fundamental properties of matter-antimatter conjugates at lowest energy and with great precision. The BASE collaboration at the antiproton decelerator of CERN is performing such high-precision comparisons with protons and antiprotons. Using advanced, ultra-stable, cryogenic particle traps and superconducting detectors with single particle sensitivity, we have performed the most precise measurement of the proton-to-antiproton charge-to-mass ratio with a fractional precision of 11 significant digits . In another measurement, we have invented a novel spectroscopy method, which allowed for the first ultra-high precision measurement of the antiproton magnetic moment with a fractional precision of 1.5 parts in a billion . Together with our recent measurement of the proton magnetic moment  this improves the precision of previous experiments  by more than a factor of 3000.
In my talk I will review the recent achievements of BASE and will outline strategies to further improve our high-precision studies of matter-antimatter symmetry. This outlook will involve the implementation of sympathetic cooling of antiprotons using quantum logic methods, as well as a motivation and first design studies for transportable antiproton traps.
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