Linear and ultrafast optical spectroscopy in the regime of the quantum Hall effect

We review our optical experiments on two-dimensional electron systems (2DES) of different mobilities, realized in modulation-doped GaAs-AlGaAs single quantum wells, in quantizing magnetic fields. The carrier densities of the 2DESs could be tuned in quite broad range between about 1 x 10(10) cm(-2) via gate electrodes. In photoluminescence (PL) and absorption experiments on 2DES with moderate mobility, at very low electron densities, we have observed the formation of negatively charged excitons, which observable at temperatures below 1k and for electron filling factors v< 1/3, i.e., in the fractional quantum Hall regime, only. In experiments where we have increased the density of the 2DES so that a uniform 2DES starts to form we have found a strong energetic anomaly of the charged excitons in the vicinity of filling factor 1/3. The anomaly could be explained by a model, assuming that at very low temperatures localised charged excitons and a uniform Laughlin liquid coexist. Furthermore, we report on ultrafast optical experiments at the v=1 quantum Hall state of a high-mobility 2DES in a GaAs-AlGaAs single quantum well. By spectrally-resolved four-wave-mixing experiments, we have investigated the coherent dynamics of photo excited electron hole pairs and found extraordinarily long decoherence times for electrons, excited into the upper spin level, around v=1. We attribute the observed faster decay of the dephasing time for v<1, as compared to v>1, presumably to the coherent coupling of the spin levels via spin waves.