Time-integrated four-wave mixing in GaN and ZnSe: Polarization-sensitive phase shift of the excitonic quantum beats

We report on the study of quantum beats in the time-integrated four-wave mixing signal in reflection geometry from a pair of excitons with different valence orbitals in GaN and ZnSe. We observe a π-phase shift between quantum beats in the co- and cross-linear polarization configuration, and nearly 100% modulation of the signal for both materials. In the co-circular polarization configuration, the observed phases of the quantum beats at the frequency of the A exciton in GaN and heavy-hole exciton in ZnSe are 0.2π and 0.1π, respectively. The phases of the quantum beats change sign for co- and counter-circular polarization configurations and also for A- (heavy-hole) and B-(light-hole) excitons in GaN(ZnSe). We describe the third-order coherent optical response of the exciton pair with different valence orbitals by taking into account the finite memory depth of the four-particle correlation. In particular, our experimental findings indicate that excitons with different valence orbitals and equal angular momentum attract each other similar to excitons with the same valence orbitals but opposite angular momentum. Excitons with different orbitals and opposite angular momenta repel one another. The comparison between experimental and theoretical results allows us to develop a quantitative analysis of the four-particle correlation in the presence of an exciton pair with different valence orbitals. We show that the observed π-phase shift and nearly 100% modulation of the signal in the co- and cross-linear polarization configuration impose restraints on the memory functions, which describe the exciton-exciton interaction. These restraints imply, in particular, that electron spins play a more important role in the exciton-exciton interaction in comparison to hole spins. We show that a striking similarity, which we observe in the quantum beat signal from GaN and ZnSe, originates from the strong four-particle correlation contribution to the third-order excitonic nonlinearity.