Direct Measurement of the Proton Magnetic Moment

The proton magnetic moment in nuclear magnetons is measured to be ${\mu }_p/{\mu }_N\equiv g/2=2.792846\pm 0.000007$, a 2.5 parts per million uncertainty. The direct determination, using a single proton in a Penning trap, demonstrates the first method that should work as well with an antiproton ($\overline{p}$) as with a proton ($p$). This opens the way to measuring the $\overline{p}$ magnetic moment (whose uncertainty has essentially not been reduced for 20 years) at least ${10}^3$ times more precisely.

Figure 1

Precision in $g_p/2$ and $g_{\overline{p}}/2$ for $p$ and $\overline{p}$ [3, 4, 5, 6].

Figure 2

(a) Analysis trap electrodes (cutaway side view) are copper with an iron ring. (b) The iron ring significantly alters $B$ on the axis. (c) Oscillating current paths (top view) for the spin flip drive. (d) An oscillating electric field (top view) drives proton cyclotron motion.

Figure 3

(a) Histogram of ${\Delta }_i$ for a nonresonant (gray histogram) and resonant (black outline histogram) spin flip drive. Half-widths of 198 and 250 mHz correspond to Allan deviations of ${\sigma }_0=60$ and ${\sigma }_f=75\mathrm{mHz}$. (b) Increase in Allan deviation with a cyclotron radius. (c) Allan deviation as a function of averaging time for a small cyclotron radius.

Figure 4

(a) Spin measurement sequence. (b) Power shift in $f_z$ due to the spin flip drive.

Figure 5

(a) The spin line. (b) The cyclotron line.