Probability of absorption and emission by an atom interacting with ultrashort laser pulses

We consider the process of transition of a two-level system to the excited state with subsequent photon emission in the presence of a laser pulse with a high degree of unipolarity. Within the framework of quantum electrodynamics, we obtain analytical expressions for the differential probability of the process depending on the temporal scales of the problem: laser pulse duration, excited-state lifetime, inverse transition frequency, and inverse frequency of the photon emitted. Besides, we calculate the total absorption probability by integrating over the three-dimensional photon momentum and summing over polarizations. We compare the results obtained for unipolar and bipolar (many-cycle) pulses.