Precision spectroscopy of the 2S-$n$P transitions in atomic hydrogen

Abstract

Precision spectroscopy of atomic hydrogen is an important way to test bound-state quantum electrodynamics (QED), one of the building blocks of the Standard Model. In its simplest form, such a test consists of the comparison of a measured transition frequency with its QED prediction, which can be calculated with very high precision for the hydrogen atom. However, these calculations require some input in the form of physical constants, such as the Rydberg constant $R_\infty$ and the proton charge radius $r_\mathrm{p}$, both of which are currently determined to a large degree by hydrogen spectroscopy itself. Therefore, the frequency of at least three different transitions needs to be measured in order to test QED. Equivalently, a comparison of the values of $R_\infty$ and $r_\mathrm{p}$ determined from measurements of different transitions constitutes a test of QED. To this end, laser spectroscopy of optical 2S-$n$P transitions has been performed in this work. As these transitions are one-photon transitions, they are affected by a different set of systematic effects than the two-photon transitions on which most other spectroscopic measurements of hydrogen are based. In order to contribute to the test of QED, their transition frequencies must be determined with a relative uncertainty on the order of one part in $10^{12}$, corresponding to approximately 1 kHz in absolute terms. This is in turn approximately a factor of 10000 smaller than the relatively broad natural linewidth of the 2S-$n$P transitions, and a successful measurement requires both a very large experimental signal-to-noise ratio and a detailed theoretical understanding of the line shape of the observed resonance. The 2S-$n$P transitions were probed on a cryogenic beam of hydrogen atoms, which were optically excited to the metastable 2S level. The atomic beam was crossed at right angles with counter-propagating spectroscopy laser beams, which further excited the atoms to the $n$P level. The fluorescence from the subsequent rapid spontaneous decay served as experimental signal. The excitation with two counter-propagating beams led to two Doppler shifts of equal magnitude, but opposite sign, which thus canceled each other out. A velocity-resolved detection was used to determine any residual Doppler shifts, which could be excluded within the measurement uncertainty for both of the measurements discussed below. In a first experiment, the 2S-4P transition was probed. Quantum interference of neighboring atomic resonances produced subtle distortions of the line shape, which were found to be significant because of the very large resolution relative to the linewidth. The line shifts caused by the distortions were directly observed and could be removed by use of a line shape model based on perturbative calculations. With this, the transition frequency was determined with a relative uncertainty of 4 parts in $10^{12}$. In combination with the very precisely measured 1S-2S transition frequency, this allowed the, at the time, most precise determination of $R_\infty$ and $r_\mathrm{p}$ from atomic hydrogen. Moreover, good agreement was found with the much more precise value of $r_\mathrm{p}$ extracted from spectroscopy of muonic hydrogen, which had been in significant disagreement with previous data from (electronic) hydrogen, causing concern about the validity of QED. This result has since been confirmed by other experiments. The 2S-4P measurement is treated in the appendix of this thesis. The 2S-4P measurement, despite its large signal-to-noise ratio, was limited by counting statistics. To improve precision, a transition with a narrower linewidth and an improved experimental signal was necessary. Hence, the study of the 2S-6P transition, which offers a three times smaller natural linewidth, was begun. The atomic beam apparatus was upgraded, resulting in a corresponding decrease of the experimentally observed linewidth, and a close to an order of magnitude larger flux of atoms in the low-velocity tail of the atomic beam. Together with a detector redesign, this led to an up to 16 times larger signal than for the 2S-4P measurement, opening the path to increased precision. The Doppler-shift suppression was also rebuilt to support such precision, including a fiber collimator developed for this purpose, which provides high-quality spectroscopy beams at the new transition wavelength of 410 nm. This enabled a measurement of the 2S-6P transition frequency with a statistical uncertainty of 430 Hz, five times lower than for the 2S-4P measurement and corresponding to a suppression of the Doppler shift by six orders of magnitude. At this level of precision, the light force shift from the diffraction of atoms at the light grating formed by the counter-propagating spectroscopy beams becomes significant. This light force shift was directly observed for the first time for the 2S-$n$P transitions and found to be well-described by a model derived for this purpose. The size of all other systematic effects, except the very precisely known recoil shift, is estimated to be below 500 Hz each. The blind data analysis is ongoing at the time of writing and thus no transition frequencies can yet be given. However, a preliminary analysis suggests a five-fold improvement in the determination of $R_\infty$ and $r_\mathrm{p}$ as compared to the 2S-4P measurement, and a two-fold improvement over the currently most precise determination from atomic hydrogen. This places the uncertainty of the determined value of $r_\mathrm{p}$ within a factor of five of that of the muonic value. The 2S-6P measurement is treated in the main text of this thesis.