Dark Matter Searches via Isotope Shift Spectroscopy with Trapped Ca⁺ Ions

We present our latest results searching for new physics beyond the Standard Model via precision isotope shift spectroscopy on the 4²S_1/2→ 3²D_3/2 (732 nm) and 4²S_1/2→ 3²D_5/2 (729 nm) electric quadrupole transitions in Ca⁺. By making measurements amongst several isotopes on multiple transitions and generating a `King Plot' it is possible to reveal contributions to the isotope shifts which do not appear at first-order in the Standard Model. Violations of `King's Linearity' thus might indicate the signature of electron-neutron couplings arising from intermediate-mass gauge bosons in the dark sector, or provide an avenue into measuring higher-order effects arising within the Standard Model, such as nuclear polarizabilities, which have previously been inaccessible to experiment. Our ongoing experiments co-trap two isotopes and simultaneously excite both ions using frequency sidebands on a single laser, dramatically reducing systematic uncertainties from many sources such as laser frequency drift and magnetic field instabilities that have limited other related experiments. Present work on the 4²S_1/2→ 3²D_3/2 transition has reached few-Hz (part-per-billion) precision, a new level of sensitivity for tests of King's Linearity.