Wave-function reconstruction in a graded semiconductor superlattice

We reconstruct a test wave function in a strongly coupled, graded well-width superlattice by resolving the spatial extension of the interband polarisation and deducing the wave function employing non-linear optical spectroscopy. The graded gap superlattice allows us to precisely control the distance between test and probe wave functions. By spatially tuning one wave function with respect to the other and recording the amplitude and the sign of the modulation of the spectrally resolved four-wave-mixing (FWM) signal with respect to delay, we are able to reconstruct the test wave function. Our numerical simulation of the third-order response of an inhomogeneously broadened system reproduces the experimental data in great detail. The wave function used for the modelling is computed by a one-dimensional transfer matrix model including electron–hole Coulomb interaction. Our experimental scheme inherently allows us to quantitatively distinguish between non-linear mechanisms leading to the FWM signal, namely phase-space filling and excitation-induced dephasing.