Theory of single-photon control from a two-level system source

We investigate the theory of a few photons on demand from a single two-level emitter excited by a square laser pulse. Using the generalized optical Bloch equations, we find exact expressions for the probability of generating zero, one, two, and three photons, the average □N□, and Mandel's Q parameter, which exhibit rich physical behaviors. The exact solution is used to design control fields that yield an optimal single- or two-photon source, under the constraints of finite laser-field strength and finite interaction time.