We present an experimental study of the lattice induced light shifts on the
1S_0-3P_0 optical clock transition (v_clock~518 THz) in neutral ytterbium. The
``magic'' frequency, v_magic, for the 174Yb isotope was determined to be 394
799 475(35)MHz, which leads to a first order light shift uncertainty of 0.38 Hz
on the 518 THz clock transition. Also investigated were the hyperpolarizability
shifts due to the nearby 6s6p 3P_0 - 6s8p 3P_0, 6s8p 3P_2, and 6s5f 3F_2
two-photon resonances at 759.708 nm, 754.23 nm, and 764.95 nm respectively. By
tuning the lattice frequency over the two-photon resonances and measuring the
corresponding clock transition shifts, the hyperpolarizability shift was
estimated to be 170(33) mHz for a linear polarized, 50 uK deep, lattice at the
magic wavelength. In addition, we have confirmed that a circularly polarized
lattice eliminates the J=0 - J=0 two-photon resonance. These results indicate
that the differential polarizability and hyperpolarizability frequency shift
uncertainties in a Yb lattice clock could be held to well below 10^-17.Comment: Accepted to PR
