Ultralight dark matter detection with trapped-ion interferometry

We explore how recent advances in the manipulation of single-ion wave packets open new avenues for detecting weak magnetic fields sourced by ultralight dark matter. A trapped ion in a ``Schr\"odinger cat'' state can be prepared with its spin and motional degrees of freedom entangled and be used as a matter-wave interferometer that is sensitive to the Aharonov-Bohm-like phase shift accumulated by the ion over its trajectory. The result of the spin-motion entanglement is a parametrically-enhanced sensitivity to weak magnetic fields as compared with an un-entangled ion in a trap. Taking into account the relevant boundary conditions, we demonstrate that a single trapped ion can probe unexplored regions of kinetically-mixed dark-photon dark matter parameter space in the $10^{-15}~\text{eV} \lesssim m_{A'} \lesssim 10^{-14}$~eV mass window. We also show how such a table-top quantum device will also serve as a complementary probe of axion-like particle dark matter in the same mass window.