Precision to the thirteenth decimal place
Experiments in hydrogen provide the most stringent test yet of quantum electrodynamics in atoms and resolve a long-standing puzzle.
Researchers at the Max Planck Institute of Quantum Optics have carried out one of the most precise tests of the Standard Model of particle physics to date. Using high-resolution hydrogen spectroscopy, they confirmed its theoretical predictions to more than twelve decimal places. The measurement provides a precise value for the proton radius, resolving the long-debated 'proton radius puzzle'. The results were recently published in Nature.
Quantum electrodynamics (QED) underpins all quantum field theories on which the Standard Model of particle physics is built and which our fundamental understanding of nature rests on. However, this model describes only around five per cent of the total matter–energy content of the universe – the “visible matter”, such as protons, neutrons and electrons, from which atoms and molecules are formed.
More than ninety-five per cent of the universe, consisting of dark matter and dark energy, remains mysterious. It may be linked to as yet unknown laws of nature, interactions or particles, so-called “new physics”. “Tiny observed variations from the expected can lead to enormous changes in our conception of the world,” explains MPQ Director Theodor Hänsch. Ultra-precise tests of QED aim to bring researchers closer to uncovering such new physics. Even if no deviations are found, the scientific value is considerable: certain hypothetical particles and interactions could then be ruled out.
Precision spectroscopy in hydrogen
A research team at the Max Planck Institute of Quantum Optics has now performed the most precise test to date of quantum electrodynamics in atoms. They investigated the 2S–6P transition in hydrogen and examined the theory to more than twelve decimal places – a level of precision made possible only through the interplay of experiment, theory and advanced computer simulations.
“The particular challenge was to achieve precision beyond twelve significant figures despite the very large natural linewidth of the transition. It’s like measuring the distance to space with a metre rule to the size of a flu virus,” explains Lothar Maisenbacher, the study’s lead author.
A major obstacle is the Doppler shift, a phenomenon familiar from everyday life: the siren of an ambulance sounds different depending on whether it is approaching or moving away. Similarly, the frequency of the laser light seen by the atoms depends on their velocity relative to the laser beam. Although cooled to minus 268 degrees Celsius, the atoms still move at the speed of a commercial aircraft. If they were to encounter the laser light at this speed, the transition frequency would already be affected at the sixth decimal place.
To cancel the Doppler shift, the scientists use two counter-propagating laser beams. One interacts with atoms moving towards it, the other with atoms moving away. When averaged, the Doppler effects cancel out – much like two ambulances whose overlapping sirens balance each other. This requires perfect reflection of the laser beams. “Developing such an optical arrangement for the violet wavelength of the 2S–6P transition was a major challenge that took us several years,” recalls co-author Vitaly Wirthl.
The counter-propagating beams also create a standing light wave that induces a so-called light force shift. “This is where quantum optics comes into play: the atoms are placed in superposition states and simultaneously ‘feel’ the nodes and antinodes of the light wave,” explains Wirthl. Although this effect appears only at the twelfth decimal place, it had to be understood in order to determine the next digit.
Proton radius puzzle resolved
The team’s measurement shows perfect agreement between experiment and theory. New interactions or previously unknown particles can be excluded down to a very small upper limit.
The measurements also provide ultra-precise values for two fundamental constants that enter the theory as parameters: the proton radius and the Rydberg constant. The new proton radius agrees with measurements in so-called muonic hydrogen – hydrogen in which the electron is replaced by a muon. Earlier comparisons between ordinary (electronic) and muonic hydrogen had revealed discrepancies, giving rise to the “proton radius puzzle”. The new measurement now rules out this discrepancy for the first time at a statistically significant level – beyond five standard deviations.
In search of “new physics“
“With this measurement, we can finally put the proton radius puzzle behind us and focus on testing QED and the Standard Model. The theories have passed this very demanding test as well, but we know they do not tell the whole story. Particularly exciting is that we are now, for the first time, observing very small and highly interesting corrections arising from interactions with more complex particles, known as hadrons,” says Lothar Maisenbacher.
Director Theodor Hänsch also emphasises the significance of the work: “Precision spectroscopy of the hydrogen atom has been an exciting adventure for more than fifty years, inspiring inventions such as laser cooling of atomic gases and optical frequency comb technology.”
The techniques presented in the study can be applied to other transitions in hydrogen and deuterium, paving the way for even more stringent tests of the Standard Model and tighter constraints on possible new forces or particles. “I find it particularly exciting to investigate whether the Standard Model still holds at this level of precision in heavy hydrogen, or deuterium. The deuterium nucleus contains an electrically neutral component that could interact very differently with hypothetical, as yet undiscovered particles or forces,” concludes Vitaly Wirthl.
