Hyperpolarizability Effects in a Sr Optical Lattice Clock

We report the observation of a higher-order frequency shift due to the trapping field in a ${}^{87}\mathrm{Sr}$ optical lattice clock. We show that, at the magic wavelength of the lattice, where the first-order term cancels, the higher-order shift will not constitute a limitation to the fractional accuracy of the clock at a level of ${10}^{-18}$. This result is achieved by operating the clock at very high trapping intensity up to $400\mathrm{kW}/{\mathrm{cm}}^2$ and by a specific study of the effect of the two two-photon transitions near the magic wavelength.