Direct Measurement of Transition Frequencies in Isolated $\overline{p}{\mathrm{H}\mathrm{e}}^{+}$ Atoms, and New $CPT$-Violation Limits on the Antiproton Charge and Mass

A radio frequency quadrupole decelerator and achromatic momentum analyzer were used to decelerate antiprotons and produce $\overline{p}{}^4\mathrm{H}\mathrm{e}^{+}$ and $\overline{p}{}^3\mathrm{H}\mathrm{e}^{+}$ atoms in ultra-low-density targets, where collision-induced shifts of the atomic transition frequencies were negligible. The frequencies at near-vacuo conditions were measured by laser spectroscopy to fractional precisions of $(6–19)\times {10}^{-8}$. By comparing these with QED calculations and the antiproton cyclotron frequency, we set a new limit of $1\times {10}^{-8}$ on possible differences between the antiproton and proton charges and masses.

Figure 1

Experimental layout. Dashed lines indicate trajectories of the antiproton beam. Drawing not to scale.

Figure 2

Energy level diagrams of $\overline{p}{}^4\mathrm{H}\mathrm{e}^{+}$ and $\overline{p}{}^3\mathrm{H}\mathrm{e}^{+}$. Wavelengths of studied transitions are indicated in nanometers.

Figure 3

Delayed annihilation time spectra of $\overline{p}{}^4\mathrm{H}\mathrm{e}^{+}$ measured at ultralow densities $\rho \sim 5\times {10}^{17}{\mathrm{c}\mathrm{m}}^{-3}$, with laser-induced annihilation spikes of the transitions $(35,33)\to (34,32)$ (a) and $(32,31)\to (31,30)$ (b). The latter transition could not be observed at higher densities.

Figure 4

Frequency profiles of $\overline{p}{}^3\mathrm{H}\mathrm{e}^{+}$ transitions $(36,34)\to (37,33)$ (a) and $(34,33)\to (35,32)$ (b). Arrows denote theoretical positions of the substructure due to spin interactions; see text.

Figure 5

Comparisons between experimental ${\nu }_{\mathrm{e}\mathrm{x}\mathrm{p}}$ (filled circles with errors) and theoretical ${\nu }_{\mathrm{t}\mathrm{h}}$ (squares [17] and triangles [13]) transition frequencies of antiprotonic helium.