AC-Stark shift

Shift has three terms: scalar, vector, and tensor. If we take frequency dependence from Budker ^[1]: $\Delta E=\frac{d\mathcal{E}_0^2}{2} \frac{\omega_a}{\omega^2_a-\omega^2_f}$ . This formula is applicable only far from resonance and it is asymmetric for red and blue detunings. For lower AC-Stark shifts it is preferable to work with blue detuning