Sensing a passage through the unknown

Since the inception of the Standard Model (SM) of particle physics half a century ago, experiments of all shapes and sizes have put it to increasingly stringent tests. The largest and most well-known are collider experiments, which in particular have enabled the direct discovery of various SM particles. Another approach utilises the tools of atomic physics. The relentless improvement in the precision of tools and techniques of atomic physics, both experimental and theoretical, has led to the verification of the SM’s predictions with ever greater accuracy. Examples include measurements of atomic parity violation that reveal the effects of the Z boson on atomic states, and measurements of atomic energy levels that verify the predictions of quantum electrodynamics (QED). Precision atomic physics experiments also include a vast array of searches for effects predicted by theories beyond-the-SM (BSM), such as fifth forces and permanent electric dipole moments that violate parity- and time-reversal symmetry. These tests probe potentially subtle yet constant (or controllable) changes of atomic properties that can be revealed by averaging away noise and controlling systematic errors.

But what if the glimpses of BSM physics that atomic spectroscopists have so painstakingly searched for over the past decades are not effects that persist over the many weeks or months of a typical measurement campaign, but rather transient events that occur only sporadically? For example, might not cataclysmic astrophysical events such as black-hole mergers or supernova explosions produce hypothetical ultralight bosonic fields impossible to generate in the laboratory? Or might not Earth occasionally pass through some invisible “cloud” of a substance (such as dark matter) produced in the early universe? Such transient phenomena could easily be missed by experimenters when data are averaged over long times to increase the signal-to-noise ratio.

Detecting such unconventional events represents several challenges. If a transient signal heralding new physics was observed with a single detector, it would be exceedingly difficult to confidently distinguish the exotic-physics signal from the many sources of noise that plague precision atomic physics measurements. However, if transient interactions occur over a global scale, a network of such detectors geographically distributed over Earth could search for specific patterns in the timing and amplitude of such signals that would be unlikely to occur randomly. By correlating the readouts of many detectors, local effects can be filtered away and exotic physics could be distinguished from mundane physics.

This idea forms the basis for the Global Network of Optical Magnetometers to search for Exotic physics (GNOME), an international collaboration involving 14 institutions from all over the world (see “Correlated” figure). Such an idea, like so many others in physics, is not entirely new. The same concept is at the heart of the worldwide network of interferometers used to observe gravitational waves (LIGO, Virgo, GEO, KAGRA, TAMA, CLIO), and the global network of proton-precession magnetometers used to monitor geomagnetic and solar activity. What distinguishes GNOME from other global sensor networks is that it is specifically dedicated to searching for signals from BSM physics that have evaded detection in earlier experiments.

GNOME is a growing network of more than a dozen optical atomic magnetometers, with stations in Europe, North America, Asia and Australia. The project was proposed in 2012 by a team of physicists from the University of California at Berkeley, Jagiellonian University, California State University – East Bay, and the Perimeter Institute. The network started taking preliminary data in 2013, with the first dedicated science-run beginning in 2017. With more data on the way, the GNOME collaboration, consisting of more than 50 scientists from around the world, is presently combing the data for signs of the unexpected, with its first results expected later this year.

Exotic-physics detectors

Optical atomic magnetometers (OAMs) are among the most sensitive devices for measuring magnetic fields. However, the atomic vapours that are the heart of GNOME’s OAMs are placed inside multi-layer shielding systems, reducing the effects of external magnetic fields by a factor of more than a million. Thus, in spite of using extremely sensitive magnetometers, GNOME sensors are largely insensitive to magnetic signals. The reasoning is that many BSM theories predict the existence of exotic fields that couple to atomic spins and would penetrate through magnetic shields largely unaffected. Since the OAM signal is proportional to the spin-dependent energy shift regardless of whether or not a magnetic field causes the energy shift, OAMs – even enclosed within magnetic shields – are sensitive to a broad class of exotic fields.

The basic principle behind OAM operation (see “Optical rotation” figure) involves optically measuring spin-dependent energy shifts by controlling and monitoring an ensemble of atomic spins via angular momentum exchange between the atoms and light. The high efficiency of optical pumping and probing of atomic spin ensembles, along with a wide array of clever techniques to minimise atomic spin relaxation (even at high atomic vapour densities), have enabled OAMs to achieve sensitivities to spin-dependent energy shifts at levels well below 10^–20 eV after only one second of integration. One of the 14 OAM installations, at California State University – East Bay, is shown in the “Benchtop physics” image.

However, one might wonder: do any of the theoretical scenarios suggesting the existence of exotic fields predict signals detectable by a magnetometer network while also evading all existing astrophysical and laboratory constraints? This is not a trivial requirement, since previous high-precision atomic spectroscopy experiments have established stringent limits on BSM physics. In fact, OAM techniques have been used by a number of research groups (including our own) over the past several decades to search for spin-dependent energy shifts caused by exotic fields sourced by nearby masses or polarised spins. Closely related work has ruled out vast areas of BSM parameter space by comparing measurements of hyperfine structure in simple hydrogen-like atoms to QED calculations. Furthermore, if exotic fields do exist and couple strongly enough to atomic spins, they could cause noticeable cooling of stars and affect the dynamics of supernovae. So far, all laboratory experiments have produced null results and all astrophysical observations are consistent with the SM. Thus if such exotic fields exist, their coupling to atomic spins must be extremely feeble.

Despite these constraints and requirements, theoretical scenarios both consistent with existing constraints and that predict effects measurable with GNOME do exist. Prime examples, and the present targets of the GNOME collaboration’s search efforts, are ultralight bosonic fields. A canonical example of an ultralight boson is the axion. The axion emerged from an elegant solution, proposed by Roberto Peccei and Helen Quinn in the late 1970s, to the strong–CP problem. The Peccei–Quinn mechanism explains the mystery of why the strong interaction, to the highest precision we can measure, respects the combined CP symmetry whereas quantum chromodynamics naturally accommodates CP violation at a level ten orders of magnitude larger than present constraints. If CP violation in the strong interaction can be described not by a constant term but rather by a dynamical (axion) field, it could be significantly suppressed by spontaneous symmetry breaking at a high energy scale. If the symmetry breaking scale is at the grand-unification-theory (GUT) scale (~10¹⁶ GeV), the axion mass is around 10^-10 eV, and at the Planck scale (10¹⁹ GeV) around 10^-13 eV – both many orders of magnitude less massive than even neutrinos. Searching for ultralight axions therefore offers the exciting possibility of probing physics at the GUT and Planck scales, far beyond the direct reach of any existing collider.

Beyond the Standard Model

In addition to the axion, there are a wide range of other hypothetical ultralight bosons that couple to atomic spins and could generate signals potentially detectable with GNOME. Many theories predict the existence of spin-0 bosons with properties similar to the axion (so-called axion-like particles, ALPs). A prominent example is the relaxion, proposed by Peter Graham, David Kaplan and Surjeet Rajendran to explain the hierarchy problem: the mystery of why the electroweak force is about 24 orders-of-magnitude stronger than the gravitational force. In 2010, Asimina Arvanitaki and colleagues found that string theory suggests the existence of many ALPs of widely varying masses, from 10^-33 eV to 10^-10 eV. From the perspective of BSM theories, ultralight bosons are ubiquitous. Some predict ALPs such as “familons”, “majorons” and “arions”. Others predict new ultralight spin-1 bosons such as dark and hidden photons. There is even a possibility of exotic spin-0 or spin-1 gravitons: while the graviton for a quantum theory of gravity matching that described by general relativity must be spin-2, alternative gravity theories (for example torsion gravity and scalar-vector-tensor gravity) predict additional spin-0 and/or spin-1 gravitons.

It also turns out that such ultralight bosons could explain dark matter. Most searches for ultralight bosonic dark matter assume the bosons to be approximately uniformly distributed throughout the dark matter halo that envelopes the Milky Way. However, in some theoretical scenarios, the ultralight bosons can clump together into bosonic “stars” due to self-interactions. In other scenarios, due to a non-trivial vacuum energy landscape, the ultralight bosons could take the form of “topological” defects, such as domain walls that separate regions of space with different vacuum states of the bosonic field (see “New domains” figure). In either of these cases, the mass-energy associated with ultralight bosonic dark matter would be concentrated in large composite structures that Earth might only occasionally encounter, leading to the sort of transient signals that GNOME is designed to search for.

Yet another possibility is that intense bursts of ultralight bosonic fields might be generated by cataclysmic astrophysical events such as black-hole mergers. Much of the underlying physics of coalescing singularities is unknown, possibly involving quantum-gravity effects far beyond the reach of high-energy experiments on Earth, and it turns out that quantum gravity theories generically predict the existence of ultralight bosons. Furthermore, if ultralight bosons exist, they may tend to condense in gravitationally bound halos around black holes. In these scenarios, a sizable fraction of the energy released when black holes merge could plausibly be emitted in the form of ultralight bosonic fields. If the energy density of the ultralight bosonic field is large enough, networks of atomic sensors like GNOME might be able to detect a signal.

In order to use OAMs to search for exotic fields, the effects of environmental magnetic noise must be reduced, controlled, or cancelled. Even though the GNOME magnetometers are enclosed in multi-layer magnetic shields so that signals from external electromagnetic fields are significantly suppressed, there is a wide variety of phenomena that can mimic the sorts of signals one would expect from ultralight bosonic fields. These include vibrations, laser instabilities, and noise in the circuitry used for data acquisition. To combat these spurious signals, each GNOME station uses auxiliary sensors to monitor electromagnetic fields outside the shields (which could leak inside the shields at a far-reduced level), accelerations and rotations of the apparatus, and overall magnetometer performance. If the auxiliary sensors indicate data may be suspect, the data are flagged and ignored in the analysis (see “Spurious signals” figure).

GNOME data that have passed this initial quality check can then be scanned to see if there are signals matching the patterns expected based on various exotic physics hypotheses. For example, to test the hypothesis that dark matter takes the form of ALP domain walls, one searches for a signal pattern resulting from the passage of Earth through an astronomical-sized plane having a finite thickness given by the ALP’s Compton wavelength. The relative velocity between the domain wall and Earth is unknown, but can be assumed to be randomly drawn from the velocity distribution of virialised dark matter, having an average speed of about one thousandth the speed of light. The relative timing of signals appearing in different GNOME magnetometers should be consistent with a single velocity v: i.e. nearby stations (in the direction of the wall propagation) should detect signals with smaller delays and stations that are far apart should detect signals with larger delays, and furthermore the time delays should occur in a sensible sequence. The energy shift that could lead to a detectable signal in GNOME magnetometers is caused by an interaction of the domain-wall field φ with the atomic spin S whose strength is proportional to the scalar product of the spin with the gradient of the field, S∙∇φ. The gradient of the domain-wall field ∇φ is proportional to its momentum relative to S, and hence the signals appearing in different GNOME magnetometers are proportional to S∙v. Both the signal-timing pattern and the signal-amplitude pattern should be consistent with a single value of v; signals inconsistent with such a pattern can be rejected as noise.

If such exotic fields exist, their coupling to atomic spins must be extremely feeble

To claim discovery of a signal heralding BSM physics, detections must be compared to the background rate of spurious false-positive events consistent with the expected signal pattern but not generated by exotic physics. The false-positive rate can be estimated by analysing time-shifted data: the data stream from each GNOME magnetometer is shifted in time relative to the others by an amount much larger than any delays resulting from propagation of ultralight bosonic fields through Earth. Such time-shifted data can be assumed to be free of exotic-physics signals, so any detections are necessarily false positives: merely random coincidences due to noise. When the GNOME data are analysed without timeshifts, to be regarded as an indication of BSM physics, the signal amplitude must surpass the 5σ threshold as compared to the background determined with the time-shifted data. This means that, for a year-long data set, an event due to noise coincidentally matching the assumed signal pattern throughout the network would occur only once every 3.5 million years.

Inspiring efforts

Having already collected over a year of data, and with more on the way, the GNOME collaboration is presently combing the data for signs of BSM physics. New results based on recent GNOME science runs are expected in 2020. This would represent the first ever search for such transient exotic spin-dependent effects. Improvements in magnetometer sensitivity, signal characterisation, and data-analysis techniques are expected to improve on these initial results over the next several years. Significantly, GNOME has inspired similar efforts using other networks of precision quantum sensors: atomic clocks, interferometers, cavities, superconducting gravimeters, etc. In fact, the results of searches for exotic transient signals using clock networks have already been reported in the literature, constraining significant parameter space for various BSM scenarios. We would suggest that all experimentalists should seriously consider accurately time-stamping, storing, and sharing their data so that searches for correlated signals due to exotic physics can be conducted a posteriori. One never knows what nature might be hiding just beyond the frontier of the precision of past measurements.