Frequency Shift Caused by Magnetic Field and Light Intensity Inhomogeneity in Optically Detected Clock

We present a novel, to the best of our knowledge, frequency shift mechanism in the optically detected atomic clock. This frequency shift is analogous to the light shift that is associated with a detecting light power. However, this shift arises from the inhomogeneity of the magnetic field (C-field) and the detecting light intensity. We call this shift the "pseudo-light shift" (p-LS). This shift allows the correlation between the clock output frequency and the detecting light power to switch between positive and negative, depending on the magnetic field. The mechanism is described and experimentally validated in our cesium beam clock through two experiments. The study of this frequency shift can enhance the accuracy of light shift assessments in atom-laser interaction systems and suppress long-term stability deterioration caused by the light power fluctuation.