${\mathrm{\chi }}^{\mathrm{}\left(5\right)\mathrm{}}$ signature in the four-wave-mixing signal from a GaAs/${\mathrm{Al}}_{0.3}$${\mathrm{Ga}}_{0.7}$As superlattice

We analyze coherent beats with a period corresponding to the biexciton binding energy in time-integrated four-wave-mixing experiments in a GaAs/${\mathrm{Al}}_{0.3}$ ${\mathrm{Ga}}_{0.7}$As superlattice at high excitation densities. Theoretical and experimental evidence is presented that the beating in the decay is a fifth-order process in the electric field, and therefore ${\mathrm{\chi }}^{\mathrm{}\left(5\right)\mathrm{}}$ contributions to the four-wave-mixing signal in the 2${\mathit{k}}_2$-${\mathit{k}}_1$ direction have to be considered for a qualitative interpretation of the measured data. In order to model the experiment we use a microscopic dynamic density-matrix theory in a real-space representation.