Polarisation and dispersion properties of light shifts in ultrastable optical frequency standards

The theoretical aspects of the Stark spectroscopy of cold alkaline-earth atoms in a three-dimensional optical lattice related to the development of ultrastable optical frequency standards of a new generation are considered. The main attention is devoted to the dispersion and polarisation properties of the light frequency shift in these atoms, which depend on the power, frequency, and polarisation of lasers forming the optical lattice. The "light-shift-cancellation" regime is considered in detail, in which the second-order dynamic Stark shifts at the forbidden clock ³P₀–¹S₀ and ³P₁–¹S₀ transitions are mutually compensated. The wavelengths at which this regime takes place ("magic" wavelengths) are calculated for the He, Be, Mg, Ca, Sr, Yb, and Hg atoms. The fourth-order dynamic susceptibilities (hyperpolarisabilities) are calculated for Sr atoms and the contribution of higher-order multipole corrections to the dynamic polarisability of the ³P₀ and ¹S₀ levels is estimated.