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Physics: Publication in Nature
The ion of the hydrogen molecule is ideally suited for making ultra-precise measurements of important physical constants. Physicists at Heinrich Heine University Düsseldorf (HHU) headed by Professor Stephan Schiller Ph.D. have now used the “Doppler-free laser spectroscopy” method for the first time on the H₂⁺ ion, achieving a huge improvement in accuracy compared with previous measurements. From this, it is also possible to determine the proton-to-electron mass ratio more accurately than ever before, as the researchers report in the journal Nature. The method paves the way for examining aspects of “new physics”.
The molecular hydrogen ion H₂⁺ is the simplest molecule. This simplicity makes it a perfect study object for physicists, as its properties – for example its energy levels – can be calculated precisely. In turn, this enables theoretical predictions to be compared with experimental measurements to determine whether the theories reflect reality correctly.
At the Institute for Experimental Physics at HHU, the research group headed by Professor Stephan Schiller Ph.D. is striving for ever greater measurement accuracy. Professor Schiller explains why: “We are searching for ‘new physics’, i.e. phenomena, which the widely successful Standard Model of particle physics cannot explain. We are comparing ultra-precise theoretical predictions for H₂⁺ with similarly precise experimental measurements to search for the tiniest discrepancies.”
Dr Soroosh Alighanbari, postdoc in the research group and lead author of a new study in Nature, adds: “Any variances we find could point to a new ‘fifth force’, which might exist beyond the four fundamental forces we know. Or we could probe the existence of hidden extra dimensions, which could influence gravity at small scales.”
The HHU research team uses quantum technologies – ion trapping, laser spectroscopy and laser frequency metrology – to measure H₂⁺ transition frequencies. Alighanbari: “In earlier work, we demonstrated the first-ever direct laser spectroscopy of a vibrational transition in H₂⁺. However, the measurement accuracy was limited by the so-called Doppler effect, which broadens spectral lines.”
The HHU physicists have now succeeded in vastly improving on the laser spectroscopy results they achieved in the past. Using a special “Doppler-free laser spectroscopy” method developed in Düsseldorf, they were able to eliminate the Doppler effect, which caused distortions in an earlier experiment. They also eliminated other distorting effects caused by external electric and magnetic fields.
“We trap both the molecular ions and laser-coolable atomic ions together,” says Alighanbari, explaining the Düsseldorf approach: “The cold atoms sympathetically cool the molecules, slowing their motion dramatically. However, as this was not yet enough to eliminate the Doppler broadening in full, we selected a special spectroscopy geometry, which made this possible.”
The physicists can use the measured vibration frequency to calculate fundamental natural constants. These numbers can be found in the equations of quantum mechanics, where they determine e.g. the energy levels of atoms and molecules. Accordingly, they also determine the frequency of absorbed or emitted light when an atom or molecule transitions between two levels.
The Düsseldorf experiment can be used to determine the ratio of proton mass (mp) to electron mass (me), as the proton mass (mp) is particularly relevant for molecules. Schiller: “The molecule spectroscopy is particularly well suited for the extremely precise determination of the proton-to-electron mass ratio (mp/me). This dimensionless constant sets the scale for particle-mass effects in molecular vibration and rotational energies.”
The researchers now present their findings in the scientific journal Nature. They determined the mp/me ratio at an uncertainty of just 26 parts per trillion, improving accuracy by three orders of magnitude compared with the earlier measurements. Alighanbari: “This result not only agrees with Penning-trap mass spectrometry, another leading technique, but even surpasses it in precision.”
“Our result is not just about mp/me. It is a stepping stone toward probing fundamental symmetries of nature, especially CPT (charge, parity, time) invariance,” says Professor Schiller, outlining the far-reaching potential of the results: “Our approach could eventually enable a much more sensitive CPT test in which we can compare a transition in H₂⁺ with its antimatter counterpart. To achieve this, however, “anti-H₂⁺” will need to be synthesised successfully at the European Organisation for Nuclear Research (CERN) in Geneva.”
Background: physics beyond the Standard Model
The Standard Model of particle physics describes fundamental particles and forces remarkably well, but profound mysteries remain unsolved: for example, the nature of dark matter – the mass of which makes up the majority of the universe – and dark energy – the effect of which drives the accelerating expansion of the universe. Further unanswered questions include: Why is gravity so weak? Why do neutrinos have mass? And why is the universe overwhelmingly made up to matter and not anti-matter?
In the future, it will be possible to compare H₂⁺ with its antimatter counterpart in order to investigate matter-antimatter asymmetry in the universe. If the molecules do not behave in exactly the same way spectroscopically – physicists refer to this as a violation of CPT invariance, which predicts that matter and antimatter should behave identically – this may permit conclusions to be drawn about why a universe filled solely with matter remained after the Big Bang.
S. Alighanbari, M. R. Schenkel, V. I. Korobov & S. Schiller. High-accuracy laser spectroscopy of H2+ and the proton-electron mass ratio. Nature 644, 69-75 (2025).
DOI: 10.1038/s41586-025-09306-2
Professor Stephan Schiller Ph.D. (left) and Dr Soroosh Alighanbari with their experiment at the Inst ...
Copyright: HHU/Nicolas Stumpe
Detailed view of the experimental setup. The hydrogen molecule ions are cooled by means of laser lig ...
Copyright: HHU/Nicolas Stumpe
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