# News: Shrinking the proton again!

Our most recent results from laser spectroscopy of the 2S-4P transition in atomic hydrogen will be published in Science in the October, 6th issue. After more than six years of work, we have succeeded in measuring the transition frequency with an uncertainty of 2.3 kHz, corresponding to a relative uncertainty of 4 parts in 1012. This is the second-best frequency measurement in hydrogen after our previous measurement of the 1S-2S transition. From these two measurements, we derive new values for the Rydberg constant and the proton root mean square (RMS) radius, {$R_\infty=10973731.568076(96)\,\mathrm{m}^{-1}$} and {$r_\mathrm{p}=0.8335(95)\,\mathrm{fm}$}, respectively. Our results are in excellent agreement with the results from laser spectroscopy of muonic hydrogen, but are 5% smaller than and disagree by 3.3 standard deviations with the hydrogen world data. More...

### Original publication

Beyer, A., Maisenbacher, L., Matveev, A., Pohl, R., Khabarova, K., Grinin, A., Lamour, T., Yost, D. C., Hänsch, T. W., Kolachevsky, N., Udem, Th.
The Rydberg constant and proton size from atomic hydrogen.
Science, 358:79, DOI: 10.1126/science.aah6677.
Supplementary materials.

### Press release

Shrinking the proton again! (english)
Und wieder schrumpft das Proton! (deutsch)

### Contact

Corresponding author: Lothar Maisenbacher
Prof. Dr. Thomas Udem

### Media

Photo showing the vacuum chamber used to measure the 2S-4P transition frequency in atomic hydrogen. The purple glow in the back stems from the microwave discharge that dissociates hydrogen molecules into hydrogen atoms. The blue light in the front is fluorescence of the vacuum viewport from the ultraviolet laser that excites the atoms to the 2S state. The turquoise blue glow is stray light from the laser system used to measure the frequency of the 2S-4P transition. (Credit: Axel Beyer / MPQ)

# Welcome to the hydrogen spectroscopy project

We are part of Prof. T. W. Hänsch's laser spectroscopy division at the Max Planck Institute of Quantum Optics (MPQ) in Garching near Munich, Germany.

Precision spectroscopy of atomic hydrogen - the most simple natural atomic system - has been one of the key tools for tests of fundamental theories eversince the dawn of modern physics. Besides fueling our basic understanding of light, matter and their interaction, it has been motivating advances in nonlinear laser spectroscopy and optical frequency metrology for more than three decades now, including the invention of the laser frequency comb technique highlighted in the citation for the 2005 Nobel Prize in physics. In particular, measurements of the 1S-2S two-photon transition frequency in hydrogen and deuterium served as a corner stone in tests of bound-state quantum electrodynamics (QED), the extraction of the Rydberg constant and the determination of fundamental constants, such as the proton root mean square (RMS) charge radius and the deuteron structure radius. In addition, our measurements were among the first laboratory experiments to set stringent limits to possible slow time variations of the fine structure constant, the fundamental parameter that scales the electromagnetic interaction.

Until a few years ago, the primary challenge in hydrogen spectroscopy has been the precise measurement of the frequency of laser light. Since the advent of the laser frequency comb technique, the challenge has moved to the understanding and control of systematic line shifts and distortions. Especially velocity-dependent effects are serious for our very light atoms that cannot be easily laser cooled. We have made major advances towards future improved measurements of the 1S-2S transition frequency. In particular, we are now routinely achieving sub-Hz line widths with diode laser systems at 972 nm and developed new tools and experimental schemes for enhanced statistics and reduced systematic uncertainties.

One of our current projects is hydrogen 2S-nP spectroscopy, aiming for a new determination of the Rydberg constant and the proton RMS charge radius from precision spectroscopy of atomic hydrogen by probing transition frequencies starting from the meta-stable 2S state to higher lying P-states. These results can shed new light on the "proton size puzzle", i.e. the discrepancy of the results for the proton RMS charge radius obtained from muonic hydrogen in 2010 on the one hand and electronic hydrogen and elastic electron-proton scattering on the other hand. So far, no satisfactory explanation has be found and suggested explanations span the entire spectrum from experimental errors up to physics beyond the standard model.

We are also working on direct frequency comb spectroscopy of two-photon transitions in hydrogen. Using a frequency comb as spectroscopy laser combines the advantages of pulsed lasers, i.e. high peak powers and efficient harmonic generation, with the advantages of CW lasers, i.e. a narrow line width and precisely defined frequency. This allows to excite ultraviolet (UV) transitions such as the 1S-3S transition at 205 nm without sacrificing precision. This experiments also serves as a test bed for spectroscopy with even shorter wavelengths in the extreme UV region.