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, $m_\chi\sim 10^{-21}\,$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 {\it 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 $m_\chi\sim 10^{-21}-10^3\,$eV, depending on the
model. We also comment on the (negligible) effect of different astrophysical
neutrino backgrounds.
