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Higher-order shifts of a clock frequency in Sr, Yb and Hg atoms trapped in an optical lattice

The recent progress in designing optical frequency standards with an uncertainty at a level of 10-17-10-18 requires unprecedented accuracy in estimating the role of higher-order uncertainties of optical clocks. In this paper, we systematically evaluate the multipole, nonlinear, anharmonic contributions to uncertainty of the optical-lattice-based clocks of alkaline-earth-like-atoms Sr, Yb and Hg.