Toward tests of QED and CPT with improved electron and positron g-factor measurements

We describe progress toward improved measurements of the electron and positron g-factors using quantum jump spectroscopy between the lowest quantum states of either particle trapped in a 100 mK cylindrical Penning trap. In a new apparatus---designed for improved stability and a better geometry for cavity-assisted sideband cooling---we have trapped a single electron, driven and observed single cyclotron transitions, and trapped positrons in a loading trap. This should enable measurements of both g-factors with better than the 0.28 ppt precision of the best electron value (the most precise measurement of a fundamental property of an elementary particle), thereby improving the positron value by a factor of more than 15.\footnote{D. Hanneke, S. Fogwell, and G. Gabrielse, PRL 100, 120801 (2008)}$^,$\footnote{R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, PRL 59, 26 (1987)} These measurements, in combination with QED theory relating the electron g-factor to $\alpha$, will improve on the most precise determination of $\alpha$, the fine structure constant. The comparison of this value with an independent measurement of $\alpha$ is the most precise test of QED. The comparison of the e$^-$ and e$^+$ g-factors will improve upon the best test of CPT symmetry in a lepton system.