Exploring the ultra-light to sub-MeV dark matter window with atomic clocks and co-magnetometers

Particle dark matter could have a mass anywhere from that of ultralight candidates, m(chi) similar to 10(-21) eV, to scales well above the GeV. Conventional laboratory searches are sensitive to a range of masses close to the weak scale, while new techniques are required to explore candidates outside this realm. In particular lighter candidates are difficult to detect due to their small momentum. Here we study two experimental set-ups which do not require transfer of momentum to detect dark matter: atomic clocks and co-magnetometers. These experiments probe dark matter that couples to the spin of matter via the very precise measurement of the energy difference between atomic states of different angular momenta. This coupling is possible (even natural) in most dark matter models, and we translate the current experimental sensitivity into implications for different dark matter models. It is found that the constraints from current atomic clocks and co-magnetometers can be competitive in the mass range m(chi) similar to 10(-21)-10(3) eV, depending on the model. We also comment on the (negligible) effect of different astrophysical neutrino backgrounds.