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Physical review. B, Condensed matter

Effects of hole burning on pulse propagation in GaAs quantum wells

John Hegarty

Published Mar 15, 1982• 46 citations
Publisher

Abstract

Pulse time-of-flight measurements at the heavy exciton resonance in GaAs quantum wells reveal large pulse delays which are dependent on intensity and pulse spectral width. The measured pulse velocities are comparable to those seen in bulk GaAs and are as low as 6.7\ifmmode\times\else\texttimes\fi{}${10}^{6}$cm${\mathrm{s}}^{\ensuremath{-}1}$. We obtain quantitative agreement with a simple theory based on hole burning observed in the inhomogeneous exciton line, and we show that the measurements are useful in estimating exciton damping, under certain conditions.

DOI
10.1103/physrevb.25.4324

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The lowest energy two-dimensional exciton in GaAs/GaAlAs multiquantum wells (MQW) is inhomogeneously broadened at low temperature by fluctuations in the layer width. The broadening permits probing of the excitons as a function of position within the inhomogeneous line[1]. At high densities interaction between the excitons becomes important and leads to saturation and to an increase of the homogeneous linewidth[2]. Using the picosecond pump/probe technique we have measured the saturation behavior as a function of exciton energy within the inhomogeneously broadened line. Figure 1 shows the transmission spectrum T of a weak narrowband probe (dotted) and the change in transmission ΔT of the probe induced by the presence of a pump for two different pump wavelength for 102 Å thick layers of GaAs separated by 200 Å layers of AlGaAs. An increase in transmission (holeburning) at the pump wavelength is observed showing that the interaction between resonant excitons is much stronger than between nonresonant excitons. The strength of the hole decreases rapidly on passing through the center of the line towards the high energy side. This is consistent with an increase in the homogeneous linewidth of the higher energy excitons[1,3]. By delaying the probe we measured the rate of decay of the hole which was found to depend strongly on pump intensity. At low intensity the hole lifetime approaches the luminescent lifetime but becomes shorter at exciton densities greater than ~109 excitons/cm2/layer. We attribute this to exciton-exciton scattering leading to spectral diffusion. The behavior was similar in 51 Å and 102 Å layers. In addition to holeburning, Figure 1 shows an increased absorption in the wings of the line whose shape is almost independent of pump wavelength and which is similar to that observed in bulk GaAs[2].

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We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 13, 2002•0 citations
Pulse time-of-flight measurements at the heavy exciton resonance in GaAs quantum wells reveal large pulse delays which are dependent on intensity and pulse spectral width. The measured pulse velocities are comparable to those seen in bulk GaAs and are as low as 6.7\ifmmode\times\else\texttimes\fi{}106{10}^{6}106cms\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1. We obtain quantitative agreement with a simple theory based on hole burning observed in the inhomogeneous exciton line, and we show that the measurements are useful in estimating exciton damping, under certain conditions.
The lowest energy two-dimensional exciton in GaAs/GaAlAs multiquantum wells (MQW) is inhomogeneously broadened at low temperature by fluctuations in the layer width. The broadening permits probing of the excitons as a function of position within the inhomogeneous line[1]. At high densities interaction between the excitons becomes important and leads to saturation and to an increase of the homogeneous linewidth[2]. Using the picosecond pump/probe technique we have measured the saturation behavior as a function of exciton energy within the inhomogeneously broadened line. Figure 1 shows the transmission spectrum T of a weak narrowband probe (dotted) and the change in transmission ΔT of the probe induced by the presence of a pump for two different pump wavelength for 102 Å thick layers of GaAs separated by 200 Å layers of AlGaAs. An increase in transmission (holeburning) at the pump wavelength is observed showing that the interaction between resonant excitons is much stronger than between nonresonant excitons. The strength of the hole decreases rapidly on passing through the center of the line towards the high energy side. This is consistent with an increase in the homogeneous linewidth of the higher energy excitons[1,3]. By delaying the probe we measured the rate of decay of the hole which was found to depend strongly on pump intensity. At low intensity the hole lifetime approaches the luminescent lifetime but becomes shorter at exciton densities greater than ~109 excitons/cm2/layer. We attribute this to exciton-exciton scattering leading to spectral diffusion. The behavior was similar in 51 Å and 102 Å layers. In addition to holeburning, Figure 1 shows an increased absorption in the wings of the line whose shape is almost independent of pump wavelength and which is similar to that observed in bulk GaAs[2].
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.
We perform femtosecond spectrally resolved pump-probe differential reflectivity measurements on excitons in GaAs quantum wells in both coherent and incoherent regimes. The spectral signal is nonzero and oscillatory at $\ensuremath{-}\mathrm{ve}$ delay up to a few ps indicating persistent coherence between excitonic polarization induced by the probe pulse and the delayed pump pulse. The signal for small +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ delay $(\ensuremath{\tau})$ shows modulation caused by quantum beats due to coexcitation of heavy and light hole excitons. The rise of the signal with $\ensuremath{\tau}$ for $\ensuremath{\tau}<0$ is rather nonexponential and is sensitive to detuning of the detection energy with respect to the exciton energy. The signal decay with $\ensuremath{\tau}$ for small +ve+ve+ve $\ensuremath{\tau}$ shows dependence on pump-probe relative polarization. The excitonic reflectivity shows a large reduction caused by excitonic absorption saturation for both +ve+ve+ve and $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}$ when the pump pulse intensity is increased to large values. To compare the experimental results with theory, we obtain an expression for the PPDR signal in terms of the third order excitonic polarization. This has an additional term not considered earlier to describe pump-probe experiments. The calculations are performed using optical Bloch equations, modified to incorporate exciton inhomogeneous broadening, quantum beats, and many body effects such as local field, excitation induced energy shift, and dephasing. These effects are found essential in explaining the observed PPDR spectral data. The delay dependence of the signal near the exciton energy is mainly controlled by inhomogeneous broadening for $\ensuremath{-}\mathrm{ve}$ $\ensuremath{\tau}.$ The signal decay for large +ve+ve+ve $\ensuremath{\tau}$ has an exponential behavior determined by the lifetime of incoherent excitons. Experiments for collinear polarization reveal an additional exponential component for small +ve+ve+ve delay. Theoretically, this is found to be related to exciton dephasing and is present only when many body effects are included.
We report the non-Markovian nature of heavy hole-heavy hole and heavy hole-light hole exciton scattering in a GaAs single quantum well. The homogeneous width depends on the exciton population, which is controlled by the delay time of phase-locked pulses. This effect is explained on the basis of excitation-induced dephasing in Markovian approximation. For short times, the homogeneous width decreases and deviates from the Markovian behavior, due to the non-Markovian behavior of the exciton-exciton scattering. We analyze the homogeneous width by using a weakly interacting boson model including the non-Markovian effect. The correlation time of the exciton-exciton scattering is estimated as 0.43 ps.
We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite 1s1s1s heavy-hole excitons in the QWs at 8 K with subpicosecond laser pulses. The excitonic polarization is probed using time integrated (TI) degenerate four wave mixing (DFWM) measurements in self-diffraction geometry. The average power density (I1){(I}_{1})(I1​) of the leading laser pulse is systematically increased to large values, keeping that of the delayed pulse small and fixed. The dephasing rate of the excitonic coherent polarization (determined by the rate of decrease of the TI-DFWM signal with delay between the exciting pulses) attains saturation at large I1{I}_{1}I1​ after an initial rise at small I1.{I}_{1}.I1​. In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with I1,{I}_{1},I1​, reaches a peak and then decreases at large I1.{I}_{1}.I1​.
We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.