Reduction of the Differential Light Shift by the Spatial Periodicity in an Optical Lattice

We study the spatial periodicity effects on the differential light shift of noninteracting atoms in an optical lattice. Through the Rabi-spectrum approach, when the wavelength of the optical lattice is not magic, a reduction to the differential light shift is expected. The reduction results from the Bloch bands induced by the quantized motion in the periodic potential. Taking the microwave transition of rubidium atoms as an example, this reduction at some wavelengths can reach one order of magnitude, compared to the data without considering the spatial profile of the optical lattice. When the atomic temperature is considered, the differential light shift increases or decreases with temperature, depending on the wavelength of the lattice. Our results should be beneficial for microwave optical lattice clock and precision measurements.