ZERO- AND ULTRALOW FIELD
NUCLEAR MAGNETIC RESONANCE

Zero- and Ultra-Low-Field (ZULF) Nuclear Magnetic Resonance (NMR) is a novel spectroscopic technique that allows for investigations of spin dynamics under the unique NMR condition of no magnetic field. This emerging modality opens a new window into the very heart of
molecular structure, where the subtle interactions between nuclear spins, known as J-couplings, take center stage, revealing exquisitely detailed chemical and structural information.

INTRODUCTION

Nuclear Magnetic Resonance (NMR) spectroscopy is a non-destructive analytical method that determines molecular structure, dynamics, and interactions by monitoring the atomic nuclei evolution in a strong magnetic field. The NMR signals (oscillating magnetic fields) are mathematically converted into spectra that report on chemical environment, connectivity and motion. From small organic molecules to proteins, batteries and porous materials, NMR has become an essential tool across chemistry, biology, medicine and materials science, and provides the physical basis for clinical MRI. 

STRONG MAGNETIC FIELD IN NMR

For several decades, progress in NMR spectroscopy has depended on the availability of ever-stronger magnets. This is associated with two factors. First, a static magnetic field removes the degeneracy of nuclear-spin energy levels. As field strength increases, the energy separation grows, producing a proportionally larger population difference between the levels at thermal equilibrium. The resulting increase in bulk magnetisation directly raises the amplitude of the NMR signal. Second, the field determines the precession frequency of the spins. Higher frequencies generate larger voltages in the detection coil through electromagnetic induction, thereby improving the signal-to-noise ratio. These considerations continue to drive efforts to construct higher-field NMR spectrometers.

DIAMAGNETIC SHIELDING AND CHEMICAL SHIFT

In NMR spectroscopy, the resonance frequency of a nucleus is modulated by the electron cloud surrounding it. Circulating electrons generate a small local magnetic field that usually counteracts, and less often reinforces, the applied field, displacing the resonance from a defined reference; this displacement is the chemical shift. Expressing shifts in parts per million removes explicit dependence on magnet strength, so spectra from 200 to 1,200 MHz can be compared directly. In absolute hertz, however, the same ppm separation widens with field strength, giving high-field magnets superior spectral dispersion. Because shielding responds to hybridisation, electronegativity, hydrogen bonding, ring currents and conformational changes, chemical shifts offer a detailed, first-line map of molecular structure.

CHALLENGES OF HIGH-FIELD NMR

While extremely powerful, the strong magnetic fields of conventional NMR present significant challenges. For one, generating such fields requires superconducting magnets maintained at cryogenic temperatures, which makes NMR spectrometers and MRI scanners bulky, costly, and maintenance-intensive. Moreover, the intense field poses safety risks: ferromagnetic objects can be violently attracted and become dangerous projectiles, and medical implants may malfunction. Uniformity of the field across the sample is also critical, as any slight inhomogeneity degrades spectral or spatial resolution. For decades, these technical, economic, and safety constraints have driven interest in interesting, yet quite exotic low-field NMR.

GNOME CAMPAIGNS

Over the years, the GNOME collaboration conducted numerous measurements campaigns. With a growing number of operational sensors, our network has reached a sensitivity of 1 pT (spin coupling recalculated into magnetic-field units) within a 100 Hz bandwidth, making the most advanced sensor of its kind. This has allowed us to search for novel dark-matter candidates and interactions, setting new limits on the pseudoscalar spin coupling between dark and ordinary matter.

DARK-MATTER DOMAIN WALLS

A specific theoretical proposal of ultralight bosonic dark matter that the GNOME collaboration has analyzed in depth is the model of a dark-matter domain structure of the so-called axion-like field (as the bosons are ultralight they manifest their exitance more as a field than individual particles). This theory proposes that fluctuations in the field in the early Universe resulted in the formation of the nonuniform field – a domain structure. Due to its nature, the scalar coupling of the field prevents from the axion-field to be detected with optical atomic magnetometers when inside individual domains. However, transition through a boundary between two domains (domain wall) generates the gradient of the field that can couple to spins and hence the filed can be detected by our netowrk of optical atomic sensors.

LIMITS ON DOMAIN WALLS

To explore the dark-matter domain structure of the axion-like field, we used the results of one of our measurement campaigns. Our search was based on identification of common transient signals from multiple magnetometers, fulfilling a specific amplitude-temporal pattern (sensors are spatially separated with their sensitive axes oriented in different directions). This allowed us to probe the mass ma and pseudoscalar coupling strength fint of axion-like particles to ordinary matter. Our results set new limits on these interactions and marked the first scientific results from GNOME. These findings demonstrate the power of the GNOME network in exploring the mysteries of dark matter.

BEYOND DOMAIN-WALL SEARCHES

While domain-wall search was the first application of GNOME, GNOME’s exploration of dark-matter models is far from being over. In the future, we will be testing other models, including the presence of dark planets, dark-matter trapped in the Earth’s gravitational field, and the emission of jets of exotic particles during catastrophic astrophysical events like black hole mergers and supernovae. The analysis of already recorded signals is underway, and the results of the searches will be presented soon.

ADVANCED GNOME

Our group works on the development of novel GNOME sensors that are highly sensitive to nonmagnetic interactions. While optical atomic magnetometers are excellent at measuring magnetic fields with extreme sensitivity, they are also susceptible to magnetic noise that affect our nonmagnetic searches. To tackle this issue, we have developed a sensor known as the self-compensating comagnetometer. This device effectively reduces low frequency noise (signal baseline drift), which has been a significant hindrance in our searches. With the implementation of this new sensor, not only will our searches be more sensitive due to the reduction in noise, but it will also enhance our searches for proton and neutron pseudoscalar spin couplings by several orders of magnitude due to the use of uncoupled nucleon gases like helium. The first incarnation of Advanced GNOME, which features several of these new sensors, began operation in 2023.

SUMMARY

GNOME is an innovative and powerful tool that provides a unique opportunity to probe the mysterious dark matter and physics beyond the Standard Model. It has been designed to enhance the sensitivity of searches for transient and oscillatory pseudoscalar spin couplings, which are used to search for evidence of exotic physics. With its state-of-the-art technology, continuous innovation, and widespread collaboration, GNOME is well positioned to make major breakthroughs in this exciting field. Its advancements will help us better understand the universe and its hidden secrets, and pave the way for new discoveries that will shape our understanding of the world we live in.

Selected publications

Selected articles:.

• M. Padniuk, E. Klinger, G. Łukasiewicz, D. Gawlian-Martin, T. H. Liu, S. Pustelny, D. F. Jackson Kimball, D. Budker, and A. Wickenbrock, Universal determination of comagnetometer response to spin coupling, Physical Review Research 6, 013339 (2024) – Full version
• Afach et al., What Can a GNOME Do? Search Targets for the Global Network of Optical Magnetometers for Exotic Physics Searches, Annalen der Physik 2023, 2300083 (2023) – Preprint
• H. Masia-Roig, N. L. Figueroa, A. Bordon, J. A. Smiga, Y. V. Stadnik, D. Budker, A. V. Gramolin, P. S. Hamilton, S. Khamis, C. A. Palm, S. Pustelny, A. O. Sushkov, A. Wickenbrock, and D. F. Jackson Kimball, Intensity interferometry for ultralight bosonic dark matter detection, Physical Review D 108, 015003 (2023).
• M. Padniuk. M. Kopciuch, R. Capolletti, A. Wickenbrock, D. Budker and S. Pustelny, Response of atomic-based sensors to magnetic and nonmagnetic perturbations, Scientific Reports 12, 324 (2022) – Full free version.
• S. Afach et al., Search for topological defect dark matter using the global network of optical magnetometers for exotic physics searches (GNOME), Nature Physics 17, 1396-1401 (2021) – Full free version.

• C. Dailey, C. Bradley, D. F. Jackson Kimball, I. A. Sulai, , A. Wickenbrock, and A. Derevianko, Quantum sensor networks as exotic field telescopes for multi-messenger astronomy, Nature Astronomy 5, 150-158 (2021) – Published version and Preprint.

Books chapters:

• A. Derivianko and S. Pustelny, Global sensor networks as probes for dark sector, In: D. F. Jackson Kimball, D.F., K. van Bibber, K. (eds) The Search for Ultralight Bosonic Dark Matter, Springer (2023) – Full free version.

Popular science:

• D. Budker, D. F. Jackson Kimball and S. Pustelny, Seeking a passage through the uknown, CERN Courier 7 (2023) – Free full version.