Evidence for Nonlinear Isotope Shift in Yb${}^{+}$ Search for New Boson

Abstract

We measure isotope shifts for five Yb${}^{+}$ isotopes with zero nuclear spin on two narrow optical quadrupole transitions ${}^2{S}_{1/2}\to {}^2{D}_{3/2}$, ${}^2{S}_{1/2}\to {}^2{D}_{5/2}$ with an accuracy of $\sim 300$ Hz. The corresponding King plot shows a $3\times 10^{-7}$ deviation from linearity at the 3 $\sigma$ uncertainty level. Such a nonlinearity can indicate physics beyond the Standard Model (SM) in the form of a new bosonic force carrier, or arise from higher-order nuclear effects within the SM. We identify the quadratic field shift as a possible contributor to the nonlinearity at the observed scale, and show how the nonlinearity pattern can be used in future, more accurate measurements to separate a new-boson signal from nuclear effects.