We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (FWM) shows biexcitonic or bound excitonic contributions under various experimental conditi ons, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through
We investigate the properties of coherent exciton states in GaAs/Al, Ga& "Asquantum wells using the four-wave-mixing technique with subpicosecond time resolution. In the first part of this work, we show that many-body interactions in a solid manifest themselves in a line shape of the four-wave-mixing signal that is substantially difterent from the predictions of the generally used simple two-level model. In particular, the coherent interaction of the quasiparticles leads to a signal at negative delay times, in agreement with recent theoretical predictions. In the second part, we report in detail about experiments where energetically close exciton transitions are excited coherently with a short laser pulse. The quantum or polarization interference leads to the observation of quantum beats in the decay of the di6'racted signal. These results demonstrate that quantum-beat spectroscopy can be applied to study intrinsic excitations in solids.
We show that a low-intensity femtosecond pulse is severely distorted while propagating through a rel-0 atively thin {( 7000 A) GaAs multiple-quantum-well sample and that this pulse distortion depends critically on the dephasing time T2 and the total thickness l. An interferometric measurement reveals the existence of well-defined nodes at which the envelope function changes its sign. This pulse distortion significantly affects femtosecond experiments such as pump-probe or four-wave-mixing experiments.In most studies of semiconductors and their nanostructures using ultrafast spectroscopy, the result are analyzed assuming that the sample is optically thin, i.e. , al &(1, where a is the absorption coefficient. With this assumption, pulse distortion can be ignored, making theoretical analysis much more manageable.However, the actual samples are very often optically thick; for instance, typical GaAs and GaAs multiple-quantum-well (MQW) samples used in transmission experiments are a few thousand A thick, making el )1. In such optically thick samples, significant pulse distortion is possible, especially when the pulse is shorter than T2. 'In GaAs quantum wells, the effects of group-velocity dispersion and hole burning on pulse propagation was studied, but due to the limited time resolution ()9 ps) and large inhomogeneous broadening, very little pulse distortion was observed. Interesting results on pulse-breaking effects have been reported for high-intensity pulses with long propagation distances. ' With the wide use of femtosecond lasers, the distortion becomes much more important especially around the exciton resonances where the pulse width is smaller than T2, and therefore, has to be considered carefully in all experiments but in extremely thin samples. However, in most transmission experiments, a timeintegrated signal is measured as a function of the time delay between the two pulses. Only recently, the time evolution of four-wave-mixing (FWM) signals has begun to provide considerable new information.In this paper, we demonstrate that a low-intensity ultrashort pulse propagating through a typical MQW sample (I approximately equal to a few thousand A) shows severe pulse distortions that depend strongly on T2 (and, therefore, homogeneous linewidth) and laser wavelengths. By comparing different samples, we show that the distortion increases dramatically with l but decreases with an increase in the inhomogeneous linewidth. Furthermore, using interferometric techniques, we probe the pulse envelope function that shows aperiodic oscillations and well-defined nodes at the exciton resonance. This demon-strates that the origin of the pulse distortion is reradiation of induced dipoles. The first principle, microscopic, coupled Maxwell-semiconductor Bloch equations (MSBE) calculation shows excellent agreements with the experiments. We also show, by time resoluing the pumpprobe experiments(TR-PP) that the pump-induced change in T2 is a primary factor in the pump-probe experiments, because the pulse distortion is sensitive to T2...
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