Tests of the Weak Equivalence Principle with Trapped Antimatter

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Abstract
Recent developments in the trapping of ions and neutral atoms suggest that significant improvements in the precision of spectroscopic measurements on such systems can be expected. The application of these techniques to trapped antiprotons, positrons and antihydrogen atoms opens up new possibilities for precision tests of the weak equivalence principle (WEP) for antimatter. It is shown that constraints on WEP for positrons and antiprotons may be imposed by comparison of electron and positron, or proton and antiproton cyclotron frequencies, or of transition frequencies in hydrogen and antihydrogen, at the same height in a gravitational potential. The constraints that may be inferred from the results of existing particle-antiparticle cyclotron frequency comparisons are derived, and the improvements which will be possible from future, higher precision experiments are analysed.

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