Extremely light and weakly interacting particles may play a crucial role in cosmology and in the ongoing search for dark matter. Unfortunately, however, these particles have so far proved very difficult to detect using existing high-energy colliders. Researchers worldwide have thus been trying to develop alternative technologies and methods that could enable the detection of these particles.

Over the past few years, collaborations between particle and atomic physicists working at different institutes worldwide have led to the development of a new technique that could be used to detect interactions between very light bosons and neutrons or electrons. Light bosons, in fact, should change the energy levels of electrons in atoms and ions, a change that could be detectable using the technique proposed by these teams of researchers.

Using this method, two different research groups (one at Aarhus University in Denmark and the other at Massachusetts Institute of Technology) recently performed experiments aimed at gathering hints of the existence of dark bosons, elusive particles that are among the most promising dark matter candidates or mediators to a dark sector. Their findings, published in Physical Review Letters, could have important implications for future dark matter experiments.

Theoretically, interactions between particles that have never been observed before, such as bosons, and other common particles (e.g., electrons), should be reflected in a discrepancy between the transition frequencies predicted by the Standard Model and those measured in actual atoms. Even if physicists are able to collect extremely precise frequency measurements, theory-based calculations for big atoms will have such a large margin of uncertainty that they cannot be reliably compared to direct measurements.

“The trick used in previous works was to perform frequency measurements of the same transitions in several isotopes of the an element, and going back to an ansatz from the ’60s (King ’63),” Elina Fuchs, a theoretical physicist at Fermilab and the University of Chicago who collaborated with the team at Aarhus University, told Phys.org. “The difference between the same transition in two different isotopes is called isotope shift. By comparing at least three such isotope shifts of at least two transitions, one does not need to rely on calculations of the frequencies in the Standard Model anymore. Instead, our method uses just the measurements, arranged in 3 data points that are each a pair of the two measured transitions frequencies in a so-called King plot. Then the question is quite simple: Do the three points lie on a straight line, as expected in the Standard Model?”

The technique used by the Aarhus team, led by Michael Drewsen, as well as by the research team at MIT led by Vladan Vuletic, essentially entails the examination of isotope shifts arranged in 4data points. If these points form a straight line, the observations are aligned with the Standard Model, which suggest that no new physics was detected. If they are not in a straight line, however, this could hint at the presence of new bosons or other physical phenomena.

Should the nonlinearity observed using this method significantly exceed the error bars set by the Standard Model, then the researchers should be able to set new bounds on the couplings and mass of the boson they may have detected. However, if it is unexpectedly large, the nonlinearity could either be associated with a boson that disturbed an electron’s energy levels or with other physical phenomena predicted by the Standard Model that are also known to break the linearity of isotope shifts.

“Looking for new bosons using King plot nonlinearity is one of a number of searches for new physics that use precision atomic or molecular experiments rather than high-energy colliders,” Julian Berengut, another theorist in the Aarhus team, who works at UNSW in Sydney, Australia, and carried out the recent study, told Phys.org. “The idea behind all of these searches is that with high precision, you can probe subtle effects from particles that you might not easily be able to detect in the colliders. Generally, these experiments are much smaller and far cheaper than collider experiments, and they provide a complementary approach. Our paper, as well as the adjacent one from Vladan Vuletic’s group at MIT, are really the first dedicated measurements collected using the King plot nonlinearity method.”

Both Vuletic’s research group and Drewsen’s team collected their measurements using a technique known as precision spectroscopy. This technique can be used to collect very precise frequency measurements in atoms, for instance recording the frequencies exhibited when an atom transitions between different states. In their experiments, the team at MIT and the researchers at Aarhus University examined different ions: ytterbium and calcium ions, respectively.

“Our main goal was to test for new forces beyond those currently known (as outlined by the Standard Model) and exclude them at a certain level,” Vladan Vuletic, the researcher who led the group at MIT, told Phys.org. “This test had been done before, but not at the precision we achieved. Simultaneously with our work, the group led by Michael Drewsen in Denmark measured similar transitions about 10 times more precisely, but in an atom with about 10 times less sensitivity to new effects than the atom we use, so the sensitivity of our experiment and Drewsen’s experiment ended up being more or less the same.”

To effectively conduct a search for dark bosons using the precision spectroscopy-based method, physicists need to measure optical transitions in different isotopes of the same element at 10¹⁵ Hz with a sub-kHz precision (i.e., with a fractional precision of 1 part in 10¹² or better). In order to do this, the particles that they will be examining should be trapped. Vuletic and his colleagues trapped the ytterbium ions they used in what is known as a ‘Paul trap’, using oscillating electric fields. They probed these ions with a very stable laser, which they stabilized using an optical resonator with highly reflective mirrors.

“We measured one isotope frequency for half an hour by scanning the laser frequency, then switched to another isotope, measured for 30 minutes, switched back to the first isotope, and averaged the measurements after every day of work,” Vuletic said. “On the next day, we would measure another isotope pair, and so on.”

As they are based on very high-precision measurements, the experiments carried out by both Vuletic and Drewsen’s groups are very difficult to perform. In fact, they require good control over both trapped ions and the different laser sources used for ionization, cooling and spectroscopy.

The team at Aarhus University gathered even more precise measurements than Vuletic’s group, reaching an unprecedented precision of 20 Hz on the ~2 THz so-called D-fine structure splitting in five Ca⁺ isotopes, which corresponds to a relative precision of 10^-11. In their experiments, they utilized a number of technological tools and techniques developed over the past century, including ion traps, laser cooling methods and a special tool known as femtosecond frequency comb laser.

“The invention of the so-called femtosecond frequency comb laser around the year 2000 is what made it possible to probe very precisely the electronic energy levels of the D-fine structure splitting, using a method that we recently demonstrated at Aarhus University,” Cyrille Solaro, one of the researchers at Aarhus University who carried out the recent study, told Phys.org. “Although not comparable in terms of size and investments to the enormous collective efforts at CERN, it is remarkable that such ‘tabletop’ experiments can contribute to explore some of the same fundamental questions in science, mainly addressing lighter particles, and significant experimental progress has happened on the short timescale of only few years.”

In addition to the remarkable and unparalleled precision, both research teams measured 4 isotope shifts using 5 different isotopes, while previous studies collected measurements for a maximum of 4 isotopes. Ultimately, their experiments allowed them to improve the bound on the coupling of a new boson to electrons and neutrons by a factor of 30 compared to the previous bound, which was also set based on a King plot of isotope shifts (i.e., using the same technique).

“Our strongly improved bound is not stronger than the existing one derived from the combination of two complementary ways of testing the couplings (neutron scattering and the magnetic moment of the electron), but it highlights the fast and significant progress achievable with the King plot method,” Fuchs said. “Furthermore, we pointed out the realistic room for further improvement of the bound if this D-fine-structure splitting transition is measured in Ca, Ba or Yb ions at the current or future precision, showing that so far untested couplings and masses can be tested with the feasible precision of 10 mHz. Such a precision will also allow for an independent test of the Be anomaly.”

While the measurements collected by the team at Aarhus University were linear and thus aligned with the Standard Model’s predictions, Vuletic’s team observed a deviation from linearity with a statistical significance of 3 sigma. While this deviation could stem from additional terms within the Standard Model, it may also hint to the existence of dark bosons.

“There is ample evidence that there is physics beyond the Standard Model (e.g., we know that there is Dark Matter in the universe), but we have no idea what constitutes this new physics,” Vuletic said. “It is important to search experimentally in different directions to exclude certain possibilities, or if one is extremely lucky, to find new physics or a new particle somewhere. We are searching for particles in an intermediate mass range, where we actually have better sensitivity than direct searches that utilize particle accelerators, as we have an extraordinary degree of control over the system at the individual-atom and quantum level.”

Both the team at MIT and the group at Aarhus University plan to conduct further searches for dark bosons and other dark matter candidates using high-resolution spectroscopy and through King plots of isotope shifts. Their work could ultimately pave the way towards the experimental observation of signals associated with dark matter.

“We will now continue our search with improved precision and on new transitions where the nonlinearities are expected to be even larger,” Vuletic said. “This will ultimately allow us to pinpoint the source of the nonlinearity we observed; whether it comes from the nuclear structure, or indeed from new physics that was previously unknown.”

In their next studies, the team at Aarhus University will try to measure isotope shifts with even greater precision, as this could allow them to set new bounds or detect new deviations from the Standard Model’s predictions. Meanwhile, the team members will also keep exploring a variety of other topics, ranging from improving precision spectroscopy and interferometry to collider physics to investigate the properties of the Higgs boson or search for new heavy particles.

“In particular, we have established contact with Prof. Hua Guan, at the Chinese Academy of Sciences in Wuhan, China, in order to initiate a collaboration aimed at improving the Ca+ King plot sensitivity by a factor ~1000,” Michael Drewsen, who led the team at Aarhus, told Phys.org. “This can be achieved through a ~1000 times more precise measurement of the D-fine structure splitting performed at Aarhus University by exploiting quantum entanglement of two ions of different isotopes, and measurements of the S-D transition with a relative precision of 10^-17 by the Wuhan-group.”

In addition to the experimental method they used so far, Fuchs and her colleagues at the Weizmann Institute of Science in Israel are considering the possibility of measuring isotope shifts of Rydberg states. This alternative version of their experiment would only require two isotopes.

“I’m extremely hopeful about the possibility of improving our experiment by taking advantage of newly-available precision studies in highly charged calcium ions,” Berengut concluded. “With this additional data, we should be able to remove any potential systematic effects and make sure that we get the most out of our King plots.”