Searching for ultra-light dark photon dark matter using optical transitions in atomic systems.

Precision measurements at atomic scales can be a powerful tool in the search for new particles that could make up the dark matter in the universe. To that end, optical transitions in atomic systems have been used previously to set leading constraints on models of dark matter than induce a time variation in the value of the fine structure "constant". We use the same systems to study an analoguous effect in a dark sector model where the Standard Model is augemented by a U(1) field which, when light enough, can constitute all the dark matter. This ultra-light dark photon does not cause a shift in the frequency of the fine-structure constant directly, but instead acts as a background electromagnetic field and induces a time varying shift in the frequency of photons emitted in transitions of ions or atoms such as Al⁺, Sr, and Yb. The latter are used as optical clocks and their transition frequency measurements have been performed to Ο( 10^-17 ) levels of relative systematic uncertainty. These experiments therefore offer unparalled sensitivity to small time-varying shifts in their respective transition frequencies. The ultra-light dark photon, acting as a background electric field, induces a tiny time varying Stark shift in the transition frequencies of, for example, Al⁺: 3s² → 3s3p or Sr: 5s² → 5s5p which can be constrained using the measured transition frequency ratio, ν_Al⁺ / v_Sr.  We exploit this to set the first direct detection constraints on dark photon dark matter lighter than 10^-15 eV and also project the sensitivity reachable by future experiments in frequency metrology, such as those using Highly Charged Ions (HCI), such dark matter candidates.