Precision Measurement of the $n=2$ Triplet $P$ $J=1$ to $J=0$ Fine Structure of Atomic Helium Using Frequency-Offset Separated Oscillatory Fields

Increasing accuracy of the theory and experiment of the $n=2$ ${}^3\mathrm{P}$ fine structure of helium has allowed for increasingly precise tests of quantum electrodynamics (QED), determinations of the fine-structure constant $\alpha$, and limitations on possible beyond the standard model physics. Here we present a 2 ppb measurement of the $J=1$ to $J=0$ interval. The measurement is performed using frequency-offset separated-oscillatory fields. Our result of 29 616 955 018(60) Hz represents a landmark for helium fine-structure measurements, and, for the first time, will allow for a 1-ppb determination of the fine-structure constant when QED theory for the interval is improved.

Figure 1

The experimental setup. An energy-level diagram (a), (not to scale) shows the 29.617-GHz interval being measured and the laser transitions used for optical pumping and for the three laser pulses ($A$, $B$, $C$). The experimental setup (b), along with an expanded view of the region where the measurement takes place (c), shows the laser and microwave interactions and ionization detection. The timing diagrams, (d) and (e), show the laser and FOSOF microwave pulses for the two timing sequences used.

Figure 2

The FOSOF line shape. The sinusoidal atomic signals for the configurations of Figs. 1 and 1 are shifted by $\mathrm{\Delta }{\theta }_{(\mathrm{d})}$ and $\mathrm{\Delta }{\theta }_{(\mathrm{e})}$ relative to a microwave beat signal, as shown in (a). $\overline{\mathrm{\Delta }\theta }=(\mathrm{\Delta }{\theta }_{(\mathrm{d})})-\mathrm{\Delta }{\theta }_{(\mathrm{e})})/2$ is shown in (b). A 300 times expanded scale in (c), where $\mathrm{\Delta }\omega T$ is subtracted, resolves the line shapes for different powers. The fits in (c) use Eq. (1), and the residuals from the fits are shown in (d),(e), and (f).

Figure 3

The extrapolation of the averaged $D=200$, $D=100$, and $D=50\mathrm{ns}$ FOSOF fit centers to $P=0$, where the center is unaffected by imperfections in the pulses. The extrapolated centers, along with their uncertainties, are shown in Fig. 4. The gray band represents the final uncertainty for the present measurement.

Figure 4

A summary of the average obtained center value for the various values of the experimental parameters. All points are extrapolations to zero power and use the frequency range $|f-f_0|<1/(2D)$, unless otherwise specified. As further discussed in the text, parts (a) through (g) show the average line centers for different $B$, $T$, $D$, $m$, $|f-f_0|$, and offset frequency and parts (h) through (l) show shifts of line centers (for $T=300$, $D=100\mathrm{ns}$, and 100% power) obtained with nonstandard parameter values (compared to similar line centers with standard parameter values). The gray band represents the final uncertainty for the present measurement.

Figure 5

A comparison of the present measurement to previous measurements [9, 14, 15, 18, 21] and to theory [48]. Corrected centers including quantum-interference effects [24, 26] are also shown with dashed error bars.