Theoretical and experimental investigation of the light shift in Ramsey coherent population trapping

The ac Stark shift (or light shift) of the 6$^{2}$S$_{1/2}$ (F $=$ 3 $\leftrightarrow $ 4) transition in $^{133}$Cs, as observed through coherent population trapping under pulsed excitation, is measured using a $^{133}$Cs gas cell and the $D_1$-line vertical-cavity surface-emitting laser. This light shift can be calculated using density-matrix analysis. We derive an expression for this shift as a function of light intensity, showing that it varies linearly with respect to light intensity only with intensities higher than 1.0~mW/cm$^2$. For pulsed excitation of high laser intensity, the variation in light shift is 20 times lower than that when using a continuous wave. The differences between the results of theory and experiment are discussed, taking into account the difference in conditions assumed; the results from theoretical analysis, taking the attenuation of the first-order sideband into account, approximately agree with the experimental results. The light shift is reduced by shortening the observation times.