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Physical review. B, Condensed matter

Femtosecond pulse distortion in GaAs quantum wells and its effect on pump-probe or four-wave-mixing experiments

D. S. KIM, Jagdeep Shah, David A. B. Miller, Theo C. Damen, A. Vinattieri, W. Schäfer, Loren N. Pfeiffer

Published Dec 15, 1994• 19 citations
Publisher

Abstract

We show that a low-intensity femtosecond pulse is severely distorted while propagating through a relatively thin (\ensuremath{\approxeq}6300 \AA{}) GaAs multiple-quantum-well sample near the exciton resonance at low temperatures. This pulse distortion depends critically on the dephasing time ${\mathit{T}}_{2}$, the total thickness l, detuning, and inhomogeneous broadening. In thinner, high-quality samples (l3000 \AA{}, exciton linewidth 1 meV), the distortion is smaller and free-induction-decay-like. An interferometric measurement reveals the existence of well-defined nodes at which the envelope function changes its sign, demonstrating that the source of the pulse distortion is the reradiation of the induced dipoles. While the effects of this pulse distortion on pump-probe or four-wave-mixing experiments are relatively small for samples with l3000 \AA{}, samples with l>6000 \AA{} are strongly affected.

DOI
10.1103/physrevb.50.18240

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jun 13, 2002•0 citations
We show that a low-intensity femtosecond pulse is severely distorted while propagating through a relatively thin (\ensuremath{\approxeq}6300 \AA{}) GaAs multiple-quantum-well sample near the exciton resonance at low temperatures. This pulse distortion depends critically on the dephasing time T2{\mathit{T}}_{2}T2​, the total thickness l, detuning, and inhomogeneous broadening. In thinner, high-quality samples (l3000 \AA{}, exciton linewidth 1 meV), the distortion is smaller and free-induction-decay-like. An interferometric measurement reveals the existence of well-defined nodes at which the envelope function changes its sign, demonstrating that the source of the pulse distortion is the reradiation of the induced dipoles. While the effects of this pulse distortion on pump-probe or four-wave-mixing experiments are relatively small for samples with l3000 \AA{}, samples with l>6000 \AA{} are strongly affected.
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.
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 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.