Probe-Field-Ellipticity-Induced Shift in an Atomic Clock

We investigate near-resonant ac-Stark shifts for optical atomic clocks, which can also be interpreted as a special class of line-pulling effects due to the Zeeman structure of atomic levels split in a dc magnetic field. This shift can arise due to residual ellipticity in the polarization of the probe field and uncertainty in the magnetic field orientation. Such a shift can have an arbitrary sign and, for some experimental conditions, can reach a fractional value of the order of ${10}^{\ensuremath{-}18}$--${10}^{\ensuremath{-}19}$, i.e., it is not negligible. Thus, it should be taken into account in the uncertainty budgets for modern ultraprecise atomic clocks. In addition, it is shown that when using hyper-Ramsey spectroscopy, this shift can be reduced to a level much lower than ${10}^{\ensuremath{-}19}$.