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Physical Review Letters

Giant excitonic resonance in time-resolved four-wave mixing in quantum wells

Dai‐Sik Kim, Jagdeep Shah, J. E. Cunningham, Theo C. Damen, Wilfried Schäfer, Michael Hartmann, Stefan Schmitt-Rink

Published Feb 17, 1992• 124 citations
Publisher

Abstract

We report a strong (300:1) excitonic resonance in time-resolved (100 fs) four-wave mixing in GaAs quantum wells as a function of the incident photon energy and show that it results from the large difference in the dephasing rates of excitons and free carriers. We conclude that excitons dominate even when they make up only a small fraction of the excited states. These results, in conjuction with new results in exciton-phonon scattering, provide new insights into previous studies performed with spectrally broad ultrashort pulses.

DOI
10.1103/physrevlett.68.1006

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We report a strong (300:1) excitonic resonance in time-resolved (100 fs) four-wave mixing in GaAs quantum wells as a function of the incident photon energy and show that it results from the large difference in the dephasing rates of excitons and free carriers. We conclude that excitons dominate even when they make up only a small fraction of the excited states. These results, in conjuction with new results in exciton-phonon scattering, provide new insights into previous studies performed with spectrally broad ultrashort pulses.
We investigate resonant time-resolved four-wave mixing on GaAs quantum wells at T=300KT=300\mathrm{K}T=300K and at elevated carrier densities using excitation with 11 fs optical pulses. The experiments are compared with non-Markovian quantum-kinetic calculations including carrier-carrier and carrier-LO-phonon scattering. A self-consistently determined two-time-dependent screened random-phase approximation Coulomb potential is used for the carrier-carrier scattering. In experiment and theory we find an unusual real-time response, which is far from an ideal photon echo. Surprisingly, we also find that the dependence of the decay time \ensuremath{\tau} of the four-wave-mixing signal versus the optically excited nonequilibrium electron-hole pair density neh{n}_{\mathrm{eh}}neh​ is quantitatively similar to the corresponding behavior of bulk GaAs. Thus both data sets can be fitted by the same form ${\ensuremath{\tau}}^{\ensuremath{-}1}={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}.$ This is not consistent with previous experimental work in a more limited range of carrier densities, which determined different behavior for quasi-two-dimensional (2D) and 3D, i.e., exponents of 0.3 and $0.55\ifmmode\pm\else\textpm\fi{}0.04,$ respectively.
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.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.
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.
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.