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Physical Review Letters

Exciton–LO-Phonon Quantum Kinetics: Evidence of Memory Effects in Bulk GaAs

L. Bányai, D. B. Tran Thoai, E. Reitsamer, H. Haug, D. Steinbach, M. U. Wehner, Martin Wegener, T. Marschner, W. Stolz

Published Sep 11, 1995• 209 citations
Publisher

Abstract

Oscillations of the transient four-wave-mixing signal with a period of about $100\mathrm{fs}$ are observed in bulk GaAs using 14 fs pulses tuned to the exciton resonance at low temperatures. The measurements are explained in terms of the non-Markovian quantum kinetics for electron-hole pairs due to LO-phonon scattering. It is shown that the observed oscillations are evidence for memory effects. The experiments provide a first test of the central ideas of quantum kinetics, in which the effects of quantum coherence and of dissipation are intrinsically connected.

DOI
10.1103/physrevlett.75.2188

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Oscillations of the transient four-wave-mixing signal with a period of about 100fs100\mathrm{fs}100fs are observed in bulk GaAs using 14 fs pulses tuned to the exciton resonance at low temperatures. The measurements are explained in terms of the non-Markovian quantum kinetics for electron-hole pairs due to LO-phonon scattering. It is shown that the observed oscillations are evidence for memory effects. The experiments provide a first test of the central ideas of quantum kinetics, in which the effects of quantum coherence and of dissipation are intrinsically connected.
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.
Summary form only given. We performed a comprehensive four-wave-mixing (FWM) study of the optical dephasing in bulk GaAs and AlGaAs with broadband 16-fs laser pulses. In contrast to previous work, spectral resolution has allowed us to unambiguously relate the decay of the coherent emission to either continuum or excitonic transitions. We have extended earlier measurements of continuum dephasing to one order of magnitude lower carrier densities. We find much shorter dephasing times and a much weaker density dependence of the dephasing than expected from the extrapolation of the high-density results. Our data indicate that a quantum kinetics model for both Coulomb and LO-phonon scattering is required to describe continuum dephasing on the 10-fs time scale at lower densities.
We have studied the coherent emission from bulk semiconductors by spectrally resolved and spectrally integrated four-wave mixing (FWM) with broadband 16-fs pulses in the carrier density range from $1\ifmmode\times\else\texttimes\fi{}{10}^{16}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$ to $6\ifmmode\times\else\texttimes\fi{}{10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ In GaAs, only continuum transitions are excited, while both excitonic and continuum transitions are excited in Al0.06Ga0.94As.{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}.Al0.06​Ga0.94​As. The decay of the FWM signal for positive time delays unambiguously reflects the dephasing of the continuum, irrespective of the excitation of excitonic transitions. We find identical ultrafast sub-20-fs decay times of the coherent emission from continuum transitions in GaAs and Al0.06Ga0.94As,{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As},Al0.06​Ga0.94​As, independent of the excess excitation energy. These decay times depend only weakly on the carrier density for densities below ${10}^{17}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}.$ The continuum dephasing is analyzed considering carrier-carrier and carrier-LO-phonon scattering in a relaxation rate approach. The excitonic transitions in Al0.06Ga0.94As{\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}Al0.06​Ga0.94​As dominate the FWM signal at negative time delays.
Summary form only given. In a coherent control four-wave mixing (FWM) experiment, a first pulse, 1, can excite a certain electron-hole pair density n/sub eh/ in a semiconductor. Because this density is connected with interband coherence, a second phase locked and time-delayed pulse, 1', adjusted for destructive interference, can lead to a coherent reemission of photons. As a result, a first light pulse has created electron-hole pairs and a second light pulse has annihilated these electron-hole pairs again. A third pulse, leads to a FWM-signal and can thus probe the remaining density. This form of coherent control has been demonstrated on excitons and on continuum transitions. In the low density regime, one can argue, however, that one merely sees the interference of two independent FWM-signals on the detector. While there is no true contradiction in theory, the latter reasoning obviously questions severely whether such experiments are really evidence for the coherent control of the carrier density.
Coherent optical phenomena such as the optical Stark effect, Rabi flopping, photon echo and quantum beating which are well-known in atomic spectroscopy can also be observed in semiconductors by using femtosecond laser pulses. On these short time scales, the quantum coherence of the optical excitations in the solid do not only influence the optical properties but change at the same time the relaxation and dephasing kinetics. The quasi-classical Boltzmann kinetics has to be replaced by quantum kinetics. Coherence leads to the appearance of memory in the scattering integrals. For femtosecond four-wave mixing and pump-and-probe spectroscopy the use of quantum kinetics for LO-phonon and for carrier-carrier scattering will be reviewed.
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.