Measurement of the $2S$ Hyperfine Interval in Atomic Hydrogen

An optical measurement of the $2S$ hyperfine interval in atomic hydrogen using two-photon spectroscopy of the $1S\mathrm{\text{−}}2S$ transition gives a value of 177 556 834.3(6.7) Hz. The uncertainty is 2.4 times smaller than achieved by our group in 2003 and more than 4 times smaller than for any independent radio-frequency measurement. The specific combination of the $2S$ and $1S$ hyperfine intervals predicted by QED theory $8f_{\mathrm{HFS}}(2S)-f_{\mathrm{HFS}}(1S)=48953(3)\mathrm{Hz}$ is in good agreement with the value of 48 923(54) Hz obtained from this experiment.

Figure 1

Experimental setup. The dye laser locked to the ULE cavity 1 in horizontal configuration serves for spectroscopy of the $1S\mathrm{\text{−}}2S$ transition in H. To switch between the singlet and the triplet transitions, the double-pass AOM frequency is changed. The 972 nm ECDL is continuously locked to the ULE cavity 2 in a vertical configuration and serves as an optical frequency reference. The beat note frequencies of 32 (triplet) and 29 MHz (singlet) are recorded by the counter simultaneously with the $1S\mathrm{\text{−}}2S$ data.

Figure 2

$2S$ HFS frequency in H evaluated for $\tau =810\mu \mathrm{s}$ using the averaged line fit. Each data point is the average over one set of measurements at unchanged conditions (particle flow, quench field 2, compensation magnetic field). The histogram shows $f_{\mathrm{HFS}}(2S)$ data for low and moderate particle flows (gray bars) and all data (white bars) except the ones taken with an inverted compensation field. The solid line is a Gaussian fit.

Figure 3

Top: Averaged experimental $f_{\mathrm{HFS}}(2S)$ results for different $\tau$ (squares). Only low- and moderate-flow data from Fig. 2 are analyzed. The gray $1\sigma$ area shows the expected frequency shift for $\Delta T=0.4\mathrm{K}$. Inset: The measured amplitude ratio of the triplet and singlet transitions which is consistent with $\Delta T=0.4\mathrm{K}$. Bottom: Mutual deviation of averaged HFS interval frequencies for different evaluation methods. Error bars are similar to the ones from the upper plot.

Figure 4

Experimental and theoretical values for the $D_{21}=8f_{\mathrm{HFS}}(2S)-f_{\mathrm{HFS}}(1S)$ difference in atomic hydrogen.