J ul 2 01 7 Two-level atom excitation probability for single-and N-photon wavepackets

We study how the transient excitation probability of a two-level atom by a quantized field depends on the temporal profile of the incident pulse, in the presence of external losses, for both coherent and Fock states, and in two complementary limits: when the pulse contains only one photon (on average), and when the number of photons N is large. For the latter case we derive analytical expressions for the scaling of the excitation probability with N that can be easily evaluated for any pulse shape.