Operational Magic Intensity for Sr Optical Lattice Clocks

We experimentally investigate the lattice-induced light shift by the electric-quadrupole (E2) and magnetic-dipole (M1) polarizabilities and the hyperpolarizability in Sr optical lattice clocks. Precise control of the axial as well as the radial motion of atoms in a one-dimensional lattice allows observing the E2-M1 polarizability difference. Measured polarizabilities determine an operational lattice depth to be 72(2)E_{R}, where the total light shift cancels to the 10^{-19} level, over a lattice-intensity variation of about 30%. This operational trap depth and its allowable intensity range conveniently coincide with experimentally feasible operating conditions for Sr optical lattice clocks.