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We present an experiment to sympathetically cool protons and antiprotons in a Penning trap by resonantly coupling the particles to laser cooled beryllium ions using a common endcap technique. Our analysis shows that preparation of (anti)protons at mK temperatures on timescales of tens of seconds is feasible. Successful implementation of the technique will have immediate and significant impact on high-precision comparisons of the fundamental properties of protons and antiprotons. This in turn will provide some of the most stringent tests of the fundamental symmetries of the Standard Model.

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