Observation of Nonlinearity of Generalized King Plot in the Search for New Boson

We measure isotope shifts for neutral Yb isotopes on an ultranarrow optical clock transition ${{}^{1}S}_0-{}^3{P}_0$ with an accuracy of a few hertz. Combined with one of the recently reported isotope-shift measurements of ${\mathrm{Yb}}^{+}$ on two optical transitions, the result allows us to construct the King plots—a set of scaled isotope shifts data on two different optical transitions plotted in two-dimensional plane. When only the leading-order terms of isotope shifts are taken into account, a King plot should exhibit a linear relation as a result of elimination of the leading nuclear-size dependence. Extremely large nonlinearity unexplainable by a quadratic field shift is revealed, which was proposed previously as a source of the observed nonlinearity of the King plot. We further construct the generalized King plot with three optical transitions so that we can eliminate the contribution arising from a higher-order effect within the standard model. 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. Under reasonable assumptions, we obtain the upper bound of the product of the couplings for a new boson, mediating a force between electrons and neutrons—$|y_e{y}_n|/(\hslash c)<1\times {10}^{-10}$ for the mass less than 1 keV—with the 95% confidence level, providing an important step toward probing new physics via isotope-shift spectroscopy.