Beyond antihydrogen: testing CPT with the molecular antihydrogen ion

Abstract

Measurements of Zeeman, Zeeman-hyperfine and ro-vibrational transitions in $\bar {H}_{2}^{-}(\bar {p}e^{+}\bar {p})$ compared to $H_{2}^{+}$ have the potential for more precise tests of CPT than can be obtained from antiprotons and antihydrogen. In particular, measurements of ro-vibrational transitions have a potential sensitivity to a difference between antiproton and proton mass three orders of magnitude higher than antihydrogen/hydrogen. Methods are outlined for precision measurements on a single $\bar {H}_{2}^{-}$ or ${H}_{2}^{+}$ ion in a cryogenic Penning trap, with non-destructive state identification using the continuous Stern-Gerlach effect or changes in mass. $\bar {H}_{2}^{-}$ can be produced using the $\bar {H}^{+}+\bar {p} \rightarrow \bar {H}_{2}^{-} + e^{+}$ reaction.