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Physical review. B, Condensed matter

Subpicosecond four-wave mixing in GaAs/ Alx Ga1−x As quantum wells

Karl Leo, Ernst Otto Göbel, Theo C. Damen, Jagdeep Shah, Stefan Schmitt-Rink, W. Schäfer, J. F. Müller, Klaus Köhler, P. Ganser

Published Sep 15, 1991• 118 citations
Publisher

Abstract

We investigate the properties of coherent exciton states in GaAs/${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells using the four-wave-mixing technique with subpicosecond time resolution. In the first part of this work, we show that many-body interactions in a solid manifest themselves in a line shape of the four-wave-mixing signal that is substantially different from the predictions of the generally used simple two-level model. In particular, the coherent interaction of the quasiparticles leads to a signal at negative delay times, in agreement with recent theoretical predictions. In the second part, we report in detail about experiments where energetically close exciton transitions are excited coherently with a short laser pulse. The quantum or polarization interference leads to the observation of quantum beats in the decay of the diffracted signal. These results demonstrate that quantum-beat spectroscopy can be applied to study intrinsic excitations in solids.

DOI
10.1103/physrevb.44.5726

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We investigate the properties of coherent exciton states in GaAs/{\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}As quantum wells using the four-wave-mixing technique with subpicosecond time resolution. In the first part of this work, we show that many-body interactions in a solid manifest themselves in a line shape of the four-wave-mixing signal that is substantially different from the predictions of the generally used simple two-level model. In particular, the coherent interaction of the quasiparticles leads to a signal at negative delay times, in agreement with recent theoretical predictions. In the second part, we report in detail about experiments where energetically close exciton transitions are excited coherently with a short laser pulse. The quantum or polarization interference leads to the observation of quantum beats in the decay of the diffracted signal. These results demonstrate that quantum-beat spectroscopy can be applied to study intrinsic excitations in solids.
We report measurements of two-photon transitions to the biexciton state and exciton-biexciton transitions (M band) in GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum wells by spectrally resolving the self-diffraction in a four-wave-mixing experiment. Furthermore, nonlinear quantum beats between a coherently prepared population of excitons and biexcitons are observed. The analysis yields a binding energy of 1.8 meV for the biexciton in 116-A\r{} quantum wells.
We present an experimental and theoretical investigation of ultrafast transient four-wave mixing of GaAs/ Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells for coherent excitation of exciton and continuum states. The signal appears at the exciton resonance and is shown to consist of two contributions: an intense spectrally narrow part only present for short time delays and a weak exponentially decaying part reflecting the intrinsic coherence properties of the exciton states. The intense part of the signal is due to the excitation of the continuum states mediated by interaction-induced nonlinearities. \textcopyright{} 1996 The American Physical Society.
Shifts in the relative phases of quantum beats in the time-resolved four-wave-mixing signals from a GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum well are observed. The relative phases are shown to depend strongly on the intensities of the incident pulses as well as their detuning from the heavy-hole exciton. A simple coupled six-level model shows that the phases of the quantum beats are directly determined by many-body effects such as density-dependent dephasing and the local-field correction.
We report time-resolved degenerate four-wave-mixing experiments on a high-quality single GaAs quantum well. The signals for parallel and cross-polarized exciting pulses show pronounced quantum beats with different frequencies corresponding to the heavy/light-hole splitting and the biexciton binding energy, respectively. Comparison of the experimental data with solutions of the optical Bloch equations for a phenomenological model system shows that these features result from strong contributions of the biexcitonic state. The importance of biexcitons to the nonlinear coherent response of the two-dimension exciton is further confirmed by the frequency dependence of the time-integrated four-wave-mixing signal amplitudes measured for the two polarization geometries.
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 have investigated, by fully-time-resolved degenerate four-wave mixing (FWM), excitonic coherence phenomena in single GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs quantum wells which are known to exhibit localization. A magnetic field (0−−12T)(0--12\phantom{\rule{0.3em}{0ex}}\mathrm{T})(0−−12T) was applied in Faraday geometry as a means of altering the nature of the excitonic transitions in a controlled manner. When the system is excited by a sequence of pulses tuned in resonance with the heavy-hole excitons, the predominant behavior observed at positive interpulse delays is beating in the FWM emission due to polarization interference between uncoupled excitons localized by monolayer islands. For negative interpulse delay the variation of beat phase with delay changes sign as the magnetic field is increased. In order to understand this feature, we modeled a coupled three-level system and included local field effects as a simple phenomenological approach to describing many-body terms. Comparison with experiments shows that with a larger magnetic field, the contribution to the signal from the coupled system reduces while that from two noninteracting two-level systems increases. We attribute this to the increased confinement of the excitons with field, leading to reduced wavefunction overlap, and hence reduced coupling.