Magic Frequencies for Cesium Primary-Frequency Standard

We consider microwave hyperfine transitions in the ground state of cesium and rubidium atoms which are presently used as the primary and the secondary frequency standards. The atoms are confined in an optical lattice generated by a circularly polarized laser field. We demonstrate that applying an external magnetic field with appropriately chosen direction may cancel dynamic Stark frequency shift making the frequency of the clock transition insensitive to the strengths of both the laser and the magnetic fields. This can be attained for practically any laser frequency which is sufficiently distant from a resonance.

Figure 1

Calculated $\cos (\theta )$ for ${}^{133}\mathrm{Cs}$, where $\theta$ is the angle between magnetic field and the light propagation which makes the laser frequency to be magic. Vertical lines correspond to frequencies of the CW ${\mathrm{CO}}_2$ laser.

Figure 2

Calculated $\cos (\theta )$ for ${}^{87}\mathrm{Rb}$.