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Physical Review Letters

Ultrafast Phase Relaxation of Excitons via Exciton-Exciton and Exciton-Electron Collisions

Lothar Schultheis, J. Kühl, A. Honold, C. W. Tu

Published Sep 29, 1986• 303 citations
Publisher

Abstract

The ultrafast relaxation of excitons in GaAs, coherently excited by a short optical pulse and subjected to collisions with free carriers and noncoherent excitons which are independently created by a second synchronized light pulse, is studied directly in the time domain by a probing of the excitonic phase coherence. The relaxation rates reveal strong exciton-exciton scattering with a collision efficiency of 1.6 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{3}$ ${\mathrm{s}}^{\ensuremath{-}1}$ and even 10 times more efficient exciton-free-carrier scattering.

DOI
10.1103/physrevlett.57.1635

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The ultrafast relaxation of excitons in GaAs, coherently excited by a short optical pulse and subjected to collisions with free carriers and noncoherent excitons which are independently created by a second synchronized light pulse, is studied directly in the time domain by a probing of the excitonic phase coherence. The relaxation rates reveal strong exciton-exciton scattering with a collision efficiency of 1.6 \ifmmode\times\else\texttimes\fi{} 10\ensuremath−4{10}^{\ensuremath{-}4}10\ensuremath−4 cm3{\mathrm{cm}}^{3}cm3 s\ensuremath−1{\mathrm{s}}^{\ensuremath{-}1}s\ensuremath−1 and even 10 times more efficient exciton-free-carrier scattering.
Ultrafast phase dynamics of free-induction decay for carriers in bulk GaAs is studied with differential-phase spectroscopy. The instantaneous phase shifts of the free-induction decay with respect to the excitation pulses are extracted from simultaneously recorded laser pulse autocorrelation and free-induction decay in GaAs. Ultrafast phase dynamics during and immediately after the femtosecond pulse excitation are numerically evaluated with optical Bloch equations using pump pulse and semiconductor exciton parameters as input. Good agreement of the theory with experiment is obtained.
Summary form only given. The coherence decay of optically excited electronic systems provides one of the most powerful tools to investigate interaction processes of excited states. In semiconductors, the optical coherence phenomena are usually investigated by nonlinear techniques such as four wave mixing (FWM), photon echo, or reflectivity experiments. Exciton-phonon, exciton-exciton, or exciton-free carriers scattering processes have been explored in recent years with these techniques. As demonstrated recently, a direct measurement of the optical dephasing time can be obtained through the temporal coherent control of electronic excitations. In these experiments, the emission following the excitation by an ultrashort optical pulse sequence, is detected in a non-specular direction (secondary emission). This provides an alternative approach to FWM techniques, which allows us to analyse the scattering processes either with phonons or due to mutual collisions. Using the coherent control technique monitored through the secondary emission (SE), we report on the coherent dynamics of excitons in bare quantum wells (QW) and compare it to that of exciton-polaritons in microcavity (MC) embedded quantum wells.
We report the coherent control of excitons in quantum wells with pairs of 150-fs infrared pulses. Oscillations in the exciton density versus inter-pump-pulse separation, which correspond to the resonant transition energy, yield new insight into coherent exciton dynamics when their phase is analyzed. We demonstrate that these oscillations are caused when the second laser pulse destroys or enhances excitons that were created by the first pulse. The coherent carrier destruction generates ultrafast exciton dynamics that are not limited by the linewidth of the optical transition.
This work presents new results of experimental studies of exciton relaxation in GaAs/AlGaAs multiple quantum well materials, using transient nonlinear laser spectroscopy techniques. In the low excitation regime, effective optical Bloch equations similar to the density matrix formalism of a two-level system describe the response. Solutions of these equations appropriate for three-pulse scattering studies are presented, along with a discussion of new experimental techniques used in this work. Non-ideal conditions present in the molecular beam epitaxy growth process introduce monolayer fluctuations in the quantum well thickness, leading to inhomogeneous broadening and exciton localization at sites of minimum energy. Localized excitons are separated in energy from extended, quasi-delocalized states by the mobility edge. Studies of localized exciton relaxation indicate that these excitons relax on a much slower timescale than delocalized excitons. The temperature dependence of the localized exciton relaxation rate shows that above 15K, the excitons are thermally activated to extended states above the mobility edge. Below 15K the excitons relax by phonon assisted migration between localization sites. For temperatures above 5K, and for exciton energies greater than 1 meV below line center, an extra dephasing mechanism characterizes the exciton relaxation. The inhomogeneous broadening of the exciton leads to the emission of stimulated photon echoes in the experimental geometry used in this work. The time-resolved emission demonstrates the stimulated photon echo nature at low excitation densities. At higher excitation densities, the decay dynamics is more complex. The time-resolved emission shows the presence of a stimulated photon echo and a free polarization decay. This unusual result suggests that both a homogeneous and an inhomogeneous exciton distribution comprise the exciton resonance. Exciton relaxation at low excitation densities represents the interaction of the exciton with the lattice. At higher excitation densities, exciton-exciton and exciton-free carrier interactions modify the relaxation rates. The dependence of the exciton relaxation rate on excitation density shows that many-body effects play an important role in the exciton physics. Free carrier interactions are more efficient at increasing the exciton relaxation rate; both types of interactions are more important in quantum well systems than in bulk materials.
Utilizing transform-limited time-resolved light scattering with simultaneously optimum temporal and spectral resolution, it is possible to investigate on a picosecond time scale energy and phase relaxation processes of excitons in semiconductors. Thereby quantum-beating as a measure of exciton coherence allows us to discriminate Raman scattering from hot luminescence as exemplified for indirect free excitons in AgBr. In order to distinguish resonant Rayleigh scattering occurring in disordered systems from ordinary fluorescence, the experimental setup has to be fully included in the theoretical description of the light scattering process. Experiments at the (n equals 1, e-hh) exciton in GaAs/AlGaAs quantum well structures confirm the predicted finite decay of this process and allow us to measure the exciton relaxation dynamics.
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.