We present analytical and numerical results for the line shapes for a two-level atom interacting with pump and probe fields. We focus our attention on a time regime which is small enough that relaxation effects could be neglected, but sufficiently large that one could integrate the signal over a large number of population oscillations between the excited and ground states. As in our earlier work [J. H. Eberly and V. D. Popov, Phys. Rev. A 37, 2012 (1988)], we consider situations where the signal is determined by the atomic inversion, and identify the transient line shape with the time-averaged inversion considered as a function of the probe frequency. We present a formulation, based on the Floquet approach, that allows us to obtain formal expressions for the transient line shape in terms of infinite continued fractions, which can be evaluated numerically. We also present line shapes computed by directly solving the equations of motion numerically and integrating the inversion numerically over long times to compare with our continued-fraction results. We discuss the dependence on initial conditions, the relative pump-probe phase, and the non-Lorentzian character of these line shapes.

• Received 25 January 1991

DOI:https://doi.org/10.1103/PhysRevA.44.1995