Prospects for Optical Clocks with a Blue-Detuned Lattice

We investigated the properties of optical lattice clocks operated with a repulsive light-shift potential. The magic wavelength, where light-shift perturbation for the clock transition cancels, was experimentally determined to be 389.889(9) nm for ${}^{87}\mathrm{Sr}$. The hyperpolarizability effects on the clock transition were investigated theoretically. With minimal trapping field perturbation provided by the blue-detuned lattice, the fractional uncertainty due to the hyperpolarizability effects was found to be $2\times {10}^{-19}$ in the relevant clock transition.