We analyze both the s- and p-wave collision induced frequency shifts and propose a over-$pi$ pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a funct
ion of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over-$pi$ pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of $10^{-18}$ in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.
We measured the absolute frequency of the optical clock transition 1S0 (F = 1/2) - 3P0 (F = 1/2) of 171Yb atoms confined in a one-dimensional optical lattice and it was determined to be 518 295 836 590 863.5(8.1) Hz. The frequency was measured agains
t Terrestrial Time (TT; the SI second on the geoid) by using an optical frequency comb of which the frequency was phase-locked to an H-maser as a flywheel oscillator traceable to TT. The magic wavelength was also measured as 394 798.48(79) GHz. The results are in good agreement with two previous measurements of other institutes within the specified uncertainty of this work.
