Four-wave mixing and terahertz emission from three-level systems in quantum wells: Effects of inhomogeneous broadening

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