CPT test with (anti-)proton magnetic moments based on quantum logic cooling and readout

Dehmelt and VanDyck's famous 1987 measurement of the electron and positron g-factor is still the most precise g-factor comparison in the lepton sector, and a sensitive test of possible CPT violation. A complementary g-factor comparison between the proton and the antiproton is highly desirable to test CPT symmetry in the baryon sector. Current experiments, based on Dehmelt's continuous Stern-Gerlach effect and the double Penning-trap technique, are making rapid progress. They are, however, extremely difficult to carry out because ground state cooling using cryogenic techniques is virtually impossible for heavy baryons, and because the continous Stern-Gerlach effect scales as $\mu$/m, where m is the mass of the particle and $\mu$ its magnetic moment. Both difficulties will ultimately limit the accuracy. We discuss experimental prospects of realizing an alternative approach to a g-factor comparison with single (anti)protons, based on quantum logic techniques proposed by Heinzen and Wineland and by Wineland et al. The basic idea is to cool, control and measure single (anti-)protons through interaction with a well-controlled atomic ion.