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

We develop the method of Ramsey spectroscopy with the use of an additional field compensating the frequency shifts of clock optical transitions. This method in combination with the method of magnetically induced excitation of strongly forbidden transitions $^1S_0$$\to$$^3P_0$ [A.V. Taichenachev, et al., Phys. Rev. Lett. {\bf 96}, 083001 (2006)] allows the practically complete compensation (down to the fractional level below 10$^{-17}$ with respect to the unperturbed clock frequency) of field shifts of various origin for even isotopes of alkaline-earth-like atoms confined to an optical lattice at magic wavelength (lattice-based atomic clocks). Apart from this, the new method can be used in the two-photon Doppler-free Ramsey spectroscopy of other forbidden optical transitions (for example, $^1S_0$$\to$$^1S_0$ and $^1S_0$$\to$$^1D_2$) and other atoms. This opens perspectives for development of principally new variants of primary optical frequency standards based on free atoms. As a whole, the method of the shift-compensating field is distinguished by simplicity and high efficiency, and it can be applied for any transitions in any atoms and ions.