Observation of non-linearity of generalized King plot in the search for new boson

We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition $^{1}\text{S}_{0}-^{3}\text{P}_{0}$ with an accuracy of a few Hz. The part-per-billion precise measurement was possible by loading the ultracold atoms into a three-dimensional magic-wavelength optical lattice and alternately interrogating the isotope pairs, thus minimizing the effects due to the optical lattice light-shift and inter-atomic interaction as well as the drifts of a clock laser frequency and a magnetic field. The determined isotope shifts, combined with one of the recently reported isotope-shift measurements of Yb$^+$ on two optical transitions, allow us to construct the King plots. Extremely large nonlinearity with the corresponding $\chi^2$ on the order of $10^4$ is revealed, and is not explained by a quadratic field shift. We further carry out the generalized King plot for three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the Standard Model which might explain the observed nonlinearity of King plots for two transitions. Our analysis of the generalized King plot shows a deviation from linearity at the 3$\sigma$ level, indicating that there exist at least two higher order contributions in the measured isotope shifts. Then, under the reasonable assumption to attribute them to higher-order field shifts within the Standard Model, we obtain the upper bound of the product of the couplings for a new boson mediating a force between electrons, and neutrons $|y_ey_n|/(\hbar c)< 1\times10^{-10}$ for the mass less than 1 keV with the 95% confidence level is derived, providing an important step towards probing new physics via isotope-shift spectroscopy.