Searching for dark matter with a 1000 km baseline interferometer

Abstract: Axion-like particles (ALPs) arise from well-motivated extensions to the Standard Model and could account for dark matter. ALP dark matter would manifest as a field oscillating at an (as of yet) unknown frequency. The frequency depends linearly on the ALP mass and plausibly ranges from $10^{-22}$ to $10$ eV/$c^2$. This motivates broadband search approaches. We report on a direct search for ALP dark matter with an interferometer composed of two atomic K-Rb-$^3$He comagnetometers, one situated in Mainz, Germany, and the other in Krak\'ow, Poland. We leverage the anticipated spatio-temporal coherence properties of the ALP field and probe all ALP-gradient-spin interactions covering a mass range of nine orders of magnitude. No significant evidence of an ALP signal is found. We thus place new upper limits on the ALP-neutron, ALP-proton and ALP-electron couplings reaching below $g_{aNN}<10^{-9}$ GeV$^{-1}$, $g_{aPP}<10^{-7}$ GeV$^{-1}$ and $g_{aee}<10^{-6}$ GeV$^{-1}$, respectively. These limits improve upon previous laboratory constraints for neutron and proton couplings by up to three orders of magnitude.