Nonlinear Isotope Shift in Yb$^{+}$ Search for Dark Matter

Recently it has been proposed to search for particles outside the Standard Model (SM) in an intermediate mass range by means of optical precision isotope shift spectroscopy. We perform such a measurement on two S $\rightarrow$ D quadrupole transitions for five isotopes of Yb $^{+}$ with zero nuclear spin with an accuracy of $\sim$ 300Hz. The corresponding King plot shows a 10 $^{ -6}$ deviation from linearity at the 3.3 $\sigma$ uncertainty level. A nonlinearity in the King plot can indicate a new-boson-mediated force beyond the Standard Model (SM), or arise from higher-order corrections within the SM. We identify the isotopic shape change of the nuclear charge distribution as a possible source of nonlinearity within the SM. We also report on progress towards more precise measurements on the quadrupole transitions and on a highly forbidden octupole transition that can be used to distinguish between effects within and outside the SM.