Optical Lattice Polarization Effects on Hyperpolarizability of Atomic Clock Transitions

The light-induced frequency shift due to hyperpolarizability (i.e., terms of second-order in intensity) is studied for a forbidden optical transition, $J=0\to J=0$. A simple universal dependence on the field ellipticity is obtained. This result allows minimization of the second-order light shift with respect to the field polarization for optical lattices operating at a magic wavelength (at which the first-order shift vanishes). We show the possibility for the existence of a magic elliptical polarization, for which the second-order frequency shift vanishes. The optimal polarization of the lattice field can be either linear, circular, or magic elliptical. The obtained results could improve the accuracy of lattice-based atomic clocks.

Figure 1

(a) Definition of the elliptical polarization parameter $\epsilon$ [see Eq. (2)]. (b) Illustration of the existence of a magic elliptical polarization ${\epsilon }_m$ [see Eq. (11)], when the coefficients $\tilde{A}(\omega )$ and $\tilde{B}(\omega )$ have opposite signs.

Figure 2

Yb energy levels responsible for the main contributions ${\beta }_e^{(1,2,3,4)}$ to the second-order shift of the forbidden transition $(6s^2){}^{1}S_0\to (6s6p){}^{3}P_0$ (all wavelengths are given in nm).