Higher-order light shifts in optical frequency standard

Higher-order perturbation theory is used to study frequency shifts of the spin-forbidden ³P_J - ¹S₀ transitions for Mg, Sr and Yb atoms in an external laser field. Calculations of the higher-order dynamic Stark effect have been performed in connection with precise measurements on cooled and trapped atoms and the design of ultra stable optical clock in an engineered light shift trap. The form of the model potential of the valence electrons suggested by Simons is used for the calculation of atomic dynamic characteristics given by second- and fourth-order perturbation theory for the interaction of the atoms with the electromagnetic field. Dispersion properties of the polarizability and hyperpolarizability components and their behavior in the vicinity of both resonances and so-called "magic wavelengths" for the upper and lower atomic states, are analyzed. Calculations of ac multipole polarizabilities and dipole hyperpolarizabilities for the ³P₀ - ¹S₀ clock transition in ⁸⁷Sr indicate that the contribution of the higher- order light shifts can be reduced to less than 1 mHz, allowing for a projected accuracy of better than 10^-17.