Magic-wave-induced ${}^1\mathbf{S}_0\text{−}{}^3\mathbf{P}_0$ transition in even isotopes of alkaline-earth-metal-like atoms

The circular polarized laser beam of the “magic” wavelength may be used for mixing the ${}^{3}P_1$ state into the long-living metastable state ${}^{3}P_0$, thus enabling the strictly forbidden ${}^{1}S_0\text{−}{}^{3}P_0$ “clock” transition in even isotopes of alkaline-earth-metal-like atoms, without a change of the transition frequency. In odd isotopes the laser beam may adjust to an optimum value the linewidth of the clock transition, originally enabled by the hyperfine mixing. We present a detailed analysis of various factors influencing resolution and uncertainty for an optical frequency standard based on atoms exposed simultaneously to the lattice standing wave and an additional “state-mixing” wave, including estimations of the “magic” wavelengths, Rabi frequencies for the clock and state-mixing transitions, ac Stark shifts for the ground and metastable states of divalent atoms.