High-Precision Measurement of the Proton’s Atomic Mass

We report on the precise measurement of the atomic mass of a single proton with a purpose-built Penning-trap system. With a precision of 32 parts per trillion our result not only improves on the current CODATA literature value by a factor of 3, but also disagrees with it at a level of about 3 standard deviations.

Figure 1

Sketch of the trap setup. The trap tower includes two separate storage traps (ST-I, ST-II), the measurement trap (MT), and a reference trap (RT) for magnetic field monitoring, which is presently not used. Ions are created in situ using a mini-EBIT [13]. By shuttling the ions between the storage traps and the MT, the time between successive measurements is minimized. Individual superconducting detection circuits for the proton (blue) and for the carbon ion (red), allow measurements at the identical electrostatic field configurations, and thus guarantee the identical position and magnetic field. For details see text.

Figure 2

Illustration of a typical dip spectrum for the determination of the proton axial frequency. The inset shows a zoom to the dip signal, together with our fitted line shape model. For details see text.

Figure 3

Illustration of the measurement sequence. In the beginning of each step, ion I is chosen randomly to exclude linear magnetic field drifts and systematic shifts arising from the measurement procedure. Ion I is then transported into the MT, and ion II into the respective storage trap. In any case, both storage traps are set to their nominal voltage to prevent systematic influence on the equilibrium position of the measured ion in the MT. After cooling the cyclotron motion as well as the axial motion, ${\nu }_{+}$ and ${\nu }_z$ are measured with the dip methods, respectively. Ten PnA cycles at different phase evolution times: 6 times 10 ms, 0.1, 1, 2, and 5 s ensure the precise determination of the initial phase and a proper phase unwrapping [20]. Then four cycles of the PnA method are applied, each with 10 s phase evolution time to determine ${\nu }_{+}$ with highest precision. Finally, ion I is moved away and ion II is loaded into the MT and its frequencies are measured in reverse order. Each such cycle gives an individual value for the mass ratio.

Figure 4

Residuals of the 3-parameter ($R_0$, $a$, $b$) fit with $R_i=R_0+a{[A_{t,i}(p)]}^2+b{[A_{t,i}({{}^{12}\mathrm{C}}^{6+})]}^2$ to the measured frequency ratios $R_i$. Here, $A_{t,i}(p)$ and $A_{t,i}({{}^{12}\mathrm{C}}^{6+})$ denote the effective dipole excitation strength, the product of excitation amplitude, and time for the modified cyclotron motion of the proton and the carbon ion, respectively. The shown modified cyclotron radii can be calculated via $r_{+,i}=\kappa \times A_{t,i}$, where the parameter $\kappa$ is extracted from $a$ and $b$, respectively. This is checked via an independent calibration of the amplitudes by means of a frequency shift due to the residual magnetic inhomogeneity and shows good agreement. The gray area indicates the prediction interval of the fit, the error bars indicate the statistical uncertainty of the individual measurement. The agreement for the complete range of modified cyclotron energies indicates the validity of our model of systematics. The data set consists of three separate ion pairs, indicated by the color of the data points. The agreement of the data sets renders an influence of parasitically trapped ions or electrons improbable.

Figure 5

Comparison of our result to previous values for the proton’s atomic mass. Mainly two Penning-trap experiments contribute to the literature value, the UW-PTMS at the University of Washington [3] and the SMILETRAP spectrometer in Stockholm [2, 4, 5]. Our value disagrees with the latest CODATA value at a level of 3.3 standard deviations.