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Physical review. B, Condensed matter

Excitonic polarization dephasing under strong resonant pulsed excitation in GaAs quantum wells

Bipul Pal, Arvind S. Vengurlekar

Published Oct 31, 2002• 6 citations
Publisher

Abstract

We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite $1s$ 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 ${(I}_{1})$ 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 ${I}_{1}$ after an initial rise at small ${I}_{1}.$ In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with ${I}_{1},$ reaches a peak and then decreases at large ${I}_{1}.$

DOI
10.1103/physrevb.66.155337

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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.
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 present a comparative study of time-integrated four-wave-mixing and femtosecond emission under resonant excitation on excitons in weakly disordered GaAs quantum wells. At highest exciton densities when dephasing dominates the spectral width (homogeneous broadening), we find that the rise time of the incoherent luminescence signal is given by TIii 2/2. At lowest densities, optical coherence times approach the exciton radiative lifetime (15 to 20 ps). This confirms our previous result that coherent resonant Rayleigh scattering is responsible for the short rise time of the excitonic emission. We also show clear evidence for dephasing due to exciton–phonon interaction, as the rise time of the emission decreases dramatically when the sample temperature is increased.
Secondary emission from GaAs quantum wells following resonant pulsed excitation is studied in the time domain. Selective excitation of heavy- and light-hole excitons is accomplished in a two-pulse excitation experiment which preserves sub-ps time resolution. After the initial rise the emission decays exponentially at a fast rate and then with another much slower exponential decay at longer times. The variations in the initial decay times with excitation density and sample temperature are similar to the variation in dephasing rates measured in four-wave mixing experiments. The decay in the visibility of heavy- and light-hole exciton beating is consistent with the decay rates measured for both species separately.
We study exciton dephasing in 8 nm GaAs quantum wells (QW) at 8 K by resonantly exciting the excitons at low densities. For this, we perform femtosecond degenerate four-wave mixing (DFWM) measurements using two laser beams. The excitons in the QWs are inhomogeneously broadened, with a photoluminescence linewidth of 1.8 meV. We investigate how the time integrated DFWM signal and its decay rate $\ensuremath{\eta}$ change as the average intensity of either of the two exciting beams is varied separately. We find that the dependence of $\ensuremath{\eta}$ on the intensity of the first pulse is about twice as that for the delayed pulse. We compare the results with a theory based on optical Bloch equations and relaxation rate approximation, accounting phenomenologically for dephasing due to exciton-exciton scattering.
We resonantly excite the n=2 excitons at 8 K in 13 nm and 17.5 nm GaAs quantum wells using 0.5 ps pulses from a Ti-Sapphire laser and perform four wave mixing (FWM) measurements. The exciton dephasing time is deduced by fitting the FWM spectra to a numerical solution of the optical Bloch equations for the excitonic resonance. The finite pulse width and presence of small inhomogeneous broadening are taken into account. The homogeneous linewidth thus obtained at different low excitation intensities has a linear dependence on the intensity. The zero intensity intercept is essentially governed by the n=2 exciton lifetime due to intersubband relaxation, the pure transverse dephasing contribution being relatively less important. We deduce the exciton lifetime to be 0.9 ps and 2.6 ps for the 13 nm and 17.5 nm QWs, respectively.