Analysis of inhomogeneous-excitation frequency shifts of ytterbium optical lattice clocks

We have investigated the frequency shifts caused by inhomogeneous excitation in a ¹⁷¹Yb optical lattice clock. The dependences of the inhomogeneity on the temperature of the cold ytterbium atoms and the misaligning angle between the lattice laser and the clock laser are analyzed by numerical calculations. The dependence of the fractional collisional frequency shift on the ground state fraction under different cold atom temperatures, atom numbers, lattice trap depths and unequal transverse and longitudinal temperatures are also shown. The results show that the uncertainty of the ytterbium clocks, contributed by the inhomogeneous excitation, can be reduced to be 10^-19 or even lower with certain conditions.