Photon statistics for a two-level system interacting with a sequence of two laser pulses

We investigate photon statistics emerging from the interaction of a two-level system with two laser pulses separated by a delay interval. It is shown that Pn (t), the probability of emitting n photons up to time t, may be represented as a summation over quantum trajectories, which allows simple identification of the coherent effect arising from the existence of the delay. We obtain a relation between photon statistics emerging from the interaction with a single pulse and photon statistics emerging from the interaction with two separated pulses with finite delay. In addition, the probabilities of emitting zero, one, and two photons, the expectation number of emissions, □N□, and Mandel's Q parameter are calculated explicitly. The case of two short and strong pulses, the so-called pump and probe setup, yielding up to two photons at most, is considered in detail. We examine different limiting behaviors of the photon statistics and obtain the upper and lower bounds for P0, P1, and P2 in the limit of strong fields. Implications for single-molecule nonlinear spectroscopy and the theory of obtaining pairs of photons on demand are discussed briefly.