An experiment underway at NPL aims to reduce the uncertainty in the Rydberg constant by making accurate measurements of two-photon transition frequencies in atomic hydrogen.

Why atomic hydrogen?

Hydrogen is unique in providing a range of calculable reference frequencies, from radio frequencies into the vacuum ultraviolet, which are linked by well-defined atomic theory and are provided by the same atomic system. The scaling factor for these transition frequencies is the Rydberg constant, which is currently known to 5 parts in 10¹².

Although the 1S – 2S transition frequency in hydrogen is known much more accurately, this is not sufficient to determine the Rydberg constant with higher accuracy. Other transition frequencies must also be measured with higher precision to disentangle quantum electrodynamic (QED) and nuclear size corrections to the energy levels.

Significantly, a recent measurement of the proton charge radius by spectroscopy of muonic hydrogen lies almost five standard deviations away from the CODATA recommended value. Assuming that the measurement is correct, this implies that either

1. the calculations of QED effects in atomic hydrogen or muonic hydrogen are incorrect or incomplete, or
2. the accepted value for the Rydberg constant is incorrect.

New high accuracy measurements of transition frequencies in atomic hydrogen have an important part to play in understanding the source of this discrepancy.

Spectroscopy of the 2S – nS and 2S – nD transitions

At NPL we have recently made the first absolute frequency measurements of the 2S – 6S and 2S – 6D transitions in atomic hydrogen.

The transitions are studied by Doppler-free two-photon spectroscopy on a hydrogen atomic beam in which the metastable atoms are produced by electron impact excitation. The transitions are excited in a collinear geometry using a frequency-stabilised Ti:sapphire laser and the absolute frequency measurements are carried out using femtosecond optical frequency combs.

The largest sources of systematic frequency shift in this experiment are the second-order Doppler shift and the ac Stark shift. The velocity distribution of the metastable atoms is measured by studying the lineshape of the Doppler-broadened single-photon 2S – 3P transition using co- and counter-propagating laser beams that are collinear with the metastable beam. The ac Stark shift is determined by recording two-photon spectra at different laser intensities. For each spectrum, we fit a theoretical line profile that takes into account the light shift and the saturation of the transition, the velocity distribution of the metastable atoms and the hyperfine structure of the upper state.

Optical excitation of the 2S state

To reduce the ac Stark shifts associated with the high laser power required to induce the two-photon transitions, we propose in a later stage of the experiment to produce the metastable 2S state by two-photon optical excitation from the ground state using a stabilised 243 nm laser source. Optical excitation, in contrast to electron impact excitation, imparts no additional momentum to the atoms and so should generate an intense, well-collimated source of metastable atoms that can be cooled to increase further the atomic density in the beam. This in turn will enable the two-photon transitions to be excited using lower laser power, reducing the light shifts.

Project team

Jeff Flowers
Patrick Josephs-Franks
Hugh Klein
Conway Langham
Helen Margolis
Louise Wright
Mark Plimmer (LCM-LNE-Cnam, Paris)
Patrick Baird (University of Oxford)
David Knight (DK Research)