Hunting Dark Matter with Atom Gradiometers

Prepared by Vincent S. H. Lee

Dark matter is one of the deepest mysteries in fundamental physics. While the existence of dark matter has been robustly established over the past decades through a combination of astronomical (e.g. the rotation of galaxies, the Bullet Cluster) and cosmological (e.g. anisotropies in the cosmic microwave background) observations, we still do not know what it is made of. Its mass could lie anywhere from an astonishingly light eV all the way up to asteroid-scale masses, spanning many orders of magnitude. Crucially, every piece of evidence we have for dark matter so far comes from a single interaction: gravity. Decades of laboratory searches have looked for additional couplings between dark matter and ordinary matter, but they are not guarenteed to exist. In a “nightmare” scenario where dark matter interacts with ordinary matter only through gravity, direct laboratory searches for dark matter would become immensely difficult since gravity is notoriously weak.

A silver lining is that another kind of detector has been under development over the past decades, with new ones set to emerge in the coming decades: gravitational wave detectors. These instruments are designed with extraordinary sensitivity to the tiniest fluctuations in spacetime, motivated by the detection of gravitational waves from merging black holes in the universe. Since dark matter certainly interacts with the detector gravitationally, these instruments can also be used as dark matter detectors, serving as a tool to probe these weak gravitational interactions. Moreover, since these experiments have been, and will be, built to understand other astrophysics, it is to our advantage to learn to harness their power for dark matter detection.

Among the most promising of these emerging detectors are those built from ultracold atoms. Atom interferometers are quantum sensors that exploit the wave nature of matter. Carefully timed laser pulses split a population of ultracold atoms into superpositions of two wavepackets, send them along different paths through spacetime, and then recombine them. Just as in an optical interferometer, the two paths accumulate a relative phase, which is exquisitely sensitive to small fluctuations in the spacetime region that the atoms experience along the way. In an atom gradiometer, two such interferometers are placed at opposite ends of a long baseline and interrogated by the same laser pulses, so that laser noise cancels and only genuine differences in the local spacetime environment remain. Proposed instruments include kilometer-scale terrestrial detectors such as AION-km and MAGIS-km, as well as space-based concepts such as MAGIS-space, AEDGE, and AEDGE+, in which pairs of satellites in Earth orbit share a baseline tens of thousands of kilometers long. These experiments are designed to open the mid-frequency gravitational-wave window between LIGO and LISA. As we show, they can also double as dark matter detectors.

In this work, we compute the purely gravitational signals that dark matter would imprint on atom gradiometers, considering both ultraheavy and ultralight dark matter. In the ultraheavy limit, dark matter may be clumped into compact objects. When such a clump streaks past the detector, its gravitational pull tugs on the freely falling atomic clouds, producing a transient phase shift. We find that a space-based gradiometer akin to AEDGE+ could detect clumps making up as little as of the local dark matter density, for clump masses in the window ~kg ~kg. In the opposite limit, ultralight dark matter behaves as a coherent classical field whose energy density and pressure oscillate at a frequency determined by its mass. These oscillations source rapid ripples in spacetime that shift the ticking rate of the atomic “clocks” in each interferometer, producing a gravitational redshift signal. Because atom gradiometers directly compare this redshift between two separated atomic ensembles, they are parametrically more sensitive to these fast-oscillating perturbations than laser interferometers such as LIGO and LISA of comparable strain sensitivity, and could probe local dark matter overdensities as small as times the average at around eV. Together, these results show that atom gradiometers, instruments built from cold atoms, might offer us a chance of detecting dark matter through gravity, the only interaction between dark and visible matter that is certain to exist.