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Nonlinear Response of Localized Excitons: Effects of the Excitation-Induced Dephasing

Paola Borri, W. Langbein, D. Birkedal, Vadim G. Lyssenko, J. M. Hvam

Published Nov 1, 1997• 8 citations
Publisher

Abstract

The polarization dependence of the ultrafast nonlinear response of localized excitons in GaAs/AlGaAs quantum wells has been investigated by spectrally resolved, transient four-wave mixing. The role of the excitation-induced dephasing in the delay dependence of the signal is discussed in detail. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay.

DOI
10.1002/1521-396x(199711)164:1<61::aid-pssa61>3.0.co;2-r

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Journal de Physique IV (Proceedings)•Oct 1, 1993•1 citation
The polarization dependence of the ultrafast nonlinear response of localized excitons in GaAs/AlGaAs quantum wells has been investigated by spectrally resolved, transient four-wave mixing. The role of the excitation-induced dephasing in the delay dependence of the signal is discussed in detail. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
Summary form only given.The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms are found to be important. First, the excitation-induced dephasing FWM signal (EID), which leads to a strong dependence of the signal on the angle between the linear input polarizations. The presence of the EID in the mainly homogeneously broadened sample (25 nm) is shown by the beating between EID and two-photon coherence (TPC) at the exciton for negative delay and co-linear polarized excitation. It vanishes for cross-polarized excitation, thus excluding the importance of local-field effects.
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.
Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time T2{\mathit{T}}_{2}T2​. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.
Recent transient four-wave-mixing experiments in the two-pulse photon-echo configuration performed on GaAs quantum wells have yielded the surprising result that in some samples the T2{\mathit{T}}_{2}T2​ time obtained from the polarization decay can be shorter for cross-polarized input fields than for parallel input fields. A concomitant change from photon-echo to free-induction-decay behavior has also been observed. A phenomenological model is presented which explains these observations by means of a disorder-induced coupling of the ${\mathrm{\ensuremath{\sigma}}}^{+}$ and ${\mathrm{\ensuremath{\sigma}}}^{\mathrm{\ensuremath{-}}}$ exciton transitions which is inhomogeneous in coupling strength. Such coupling also leads to a remarkable change in the light-hole--heavy-hole exciton quantum beat phase as a function of pulse delay for a critical relative orientation of the polarization of the incident pulses. Experimental observations of this effect are presented to support the validity of the model.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.