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Coherent control of carrier-carrier scattering in bulk GaAs in the regime of Coulomb quantum kinetics

Werner Hügel, S. Chatterjee, Martin Wegener

Published May 7, 2000• 0 citations
OpenAlex

Abstract

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.

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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.
Summary form only given. Here, we use the polarization selection rules for four-wave mixing (FWM) and a test that was originally designed to distinguish between quantum beats and polarization interference to demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells. We show that when the four-wave-mixing signal is produced by two pulses having the same circular polarizations that quantum-beat-like behavior is observed. The latter observation is contrary to the predictions based on either the density matrix equations for two independent three-level systems (without many body effects) or the conventional semiconductor Bloch equations (SBE), both of which predict that polarization interference, but not quantum beats, should be observed. Consequently, these observations provide clear evidence for exciton-exciton correlations and evidence that those correlations go beyond those contained in the SBE. The procedure described here provides a simple effective test for such processes. Finally, we show that the quantum-beating-like behavior can be reproduced by including a density-dependent dephasing term (so-called excitation-induced dephasing, or EID) in the density matrix equations.
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.
The interband polarization induced by two phase-locked pulses in a semiconductor shows strong interference effects depending on the time, ${\ensuremath{\tau}}_{1},$ separating the pulses. The four-wave mixing signal diffracted from a third pulse delayed by $\ensuremath{\tau}$ is coherently controlled by tuning ${\ensuremath{\tau}}_{1}.$ The four-wave mixing response is evaluated exactly for a two-level system coupled to a single LO phonon. In the weak coupling regime it shows oscillations with the phonon frequency which turn into sharp peaks at multiples of the phonon period for a larger coupling strength. Destructive interferences between the two phase-locked pulses produce a splitting of the phonon peaks into a doublet. For fixed $\ensuremath{\tau}$ but varying ${\ensuremath{\tau}}_{1},$ the signal shows rapid oscillations at the interband transition frequency, whose amplitude exhibits bursts at multiples of the phonon period.
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.
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.
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.