  Using a perturbation theory based on the density-matrix formulation, we study
the nonlinear optical responses of a noninteracting three-level model system to
consecutive coherent pulsed excitations, as realized in several recent
experiments involving excitonic transitions in quantum wells. The terahertz
emission, which is a second order response, and the four-wave mixing signal, a
third order response, are calculated within the rotating-wave approximation, in
the presence of detuning, dephasing, and inhomogeneous broadening. We study the
quantum beats in the photon echo from transient four-wave mixing experiments of
a three-level system. We find that the temporal profile of the photon echo
signal in the four-wave mixing experiments depends very strongly on the amount
of inhomogeneous broadening of the energy levels involed. Both the position and
the intensity of the peaks exhibit a smooth evolution from strong quantum beats
to a conventional photon echo as the inhomogeneous broadening increases. These
features from our noninteracting model system are compared with a recent
experiment, and found to account for a number of experimental observations.
