4-WAVE-MIXING THEORY BEYOND THE SEMICONDUCTOR BLOCH EQUATIONS

Four-wave-mixing (FWM) experiments using a dynamical density matrix mo del of the semiconductor band edge are discussed. Higher-order correla tion functions are retained which are neglected in the commonly used R PA treatment leading to the semiconductor Bloch equations. In order to terminate the hierarchy of the equations of motion for the higher-ord er density matrices systematically a truncation scheme controlled by o rders in the driving field is applied. For any prescribed order n in t he exciting field a closed set of equations is obtained from which the dielectric response up to order n can be calculated exactly. In addit ion it turns out that in a coherently driven system part of the remain ing density matrices become redundant and can be eliminated. Four-wave -mixing experiments are dominated by third-order contributions. Applyi ng the above-described results one ends up with only two functions in this case. These are the excitonic and the biexcitonic transition dens ities. As an application of our method the example of a GaAs single qu antum well is studied. Two pulses with finite lengths are assumed such that both heavy-acid light-hole excitons are excited. The influence o f the biexciton contribution on the polarization properties of the FWM signal is analyzed and compared with experimental results.