The standard picture of dark matter is one of individual particles: annihilating with each other, bumping into nuclei or electrons in direct detection experiments, or being produced from particle collisions. This is a good description if the dark matter mass is larger than a few electron-volts (eV). But if the dark matter is much lighter, and is a boson rather than a fermion, quantum mechanics tells us that the dark matter particles lose their individual identities and start behaving collectively, as a field. In fact, there is so much dark matter that the quantum nature of this field is not apparent, and it can behave like a classical field. Photons do exactly the same thing: the light from your computer screen that allows you to read this text is best described by an electromagnetic field which satisfies Maxwell’s equations, rather than by individual photons. As a consequence, the intuition for experiments to look for coherent-field dark matter requires thinking about charges and currents, rather than individual scattering events.

The axion is a dark matter candidate which can satisfy all the required properties to behave as a coherent field. There are lots of reasons to expect ultralight axions, both experimental and theoretical. The observation that an electric dipole moment for the neutron has not yet been detected, despite the fact that it is easy to write down a term which would generate one, is known as the “strong CP problem.” An ultralight axion could solve this problem by essentially cancelling off this extra term. Highbrow theoretical arguments from string theory also suggest the existence of axions, maybe even hundreds or thousands of them, which arise from the extra dimensions required by string theory.

Generically, axions will interact very weakly with electromagnetism, which suggests a detection strategy: in a strong magnetic field, the axion field will source a very weak response magnetic field. Along with colleagues at MIT, I proposed a design for an experiment, “ABRACADABRA,” to detect axion dark matter, which exploits advances from totally different fields (MRI research in medical physics, and ultra-sensitive current measurement in metrology) to search for axions over a wide range of masses. The first results from this experiment were posted to the arXiv in December 2018, and our second-run analysis was completed in 2021. The ABRACADBRA collaboration is currently merging with the DM Radio collaboration to build a larger, more sensitive version of the experiment. My group also showed that if we were able to build two such experiments, we could exploit the spatial correlations between them to detect the wavelike nature of the axion field and determine its full three-dimensional velocity distribution.

I have also proposed an experiment to look for axions which might not make up dark matter, by looking for photon-photon scattering (equivalently, nonlinearities in Maxwell’s equations) mediated by axions in superconducting cavities. This is simultaneously more general (one can look for axions of many masses simultaneously, rather than just the species which make up dark matter) and more limited (if we find a signal, it doesn’t necessarily tell us anything about dark matter) than the ABRACADABRA program, which makes it nicely complementary. This work is being pursued with SQMS at Fermilab, which makes the best superconducting cavities in the world.

Axion dark matter can also interact with condensed matter systems in fascinating ways. The gradient of the axion field looks, for all intents and purposes, like a very weak magnetic field, which may couple to nuclear spins and make them precess as in a nuclear magnetic resonance experiment. A very peculiar phase of superfluid helium-3, the homogeneous precession domain, features a macroscopically-coherent magnetic moment that slowly drifts in precession frequency. As this frequency crosses the frequency corresponding to the axion mass, it may cause a “blip” which could be read out with quantum sensors and atomic clocks. The combination of precision metrology, particle physics, and condensed matter physics required to study axions makes this a very exciting area of research, with many new ideas on the horizon.

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