Optical Stark effect and photon statistics in the density matrix approach

We analyse a pump-probe set-up for detecting the optical Stark effect on two-level atoms with a quantized pump field in terms of a density matrix approach (DMA). The approximation used reveals a method to calculate the probe absorption spectra without high computational effort. It is even applicable for large numbers of atoms where the exact calculation is not practicable. The probe spectra in the DMA reflect the photon statistics of the pump field and deviate only slightly from exact results for relevant experimental parameters.