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We develop the method of Ramsey spectroscopy with the use of an additionalfield compensating the frequency shifts of clock optical transitions. Thismethod in combination with the method of magnetically induced excitation ofstrongly forbidden transitions $^1S_0$$\to$$^3P_0$ [A.V. Taichenachev, et al.,Phys. Rev. Lett. {\bf 96}, 083001 (2006)] allows the practically completecompensation (down to the fractional level below 10$^{-17}$ with respect to theunperturbed clock frequency) of field shifts of various origin for evenisotopes of alkaline-earth-like atoms confined to an optical lattice at magicwavelength (lattice-based atomic clocks). Apart from this, the new method canbe used in the two-photon Doppler-free Ramsey spectroscopy of other forbiddenoptical transitions (for example, $^1S_0$$\to$$^1S_0$ and $^1S_0$$\to$$^1D_2$)and other atoms. This opens perspectives for development of principally newvariants of primary optical frequency standards based on free atoms. As awhole, the method of the shift-compensating field is distinguished bysimplicity and high efficiency, and it can be applied for any transitions inany atoms and ions.

Field Compensation of Field Frequency Shifts in the Ramsey Spectroscopy of Clock Optical Transitions