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Physical Review Letters

Coherent dynamics of excitonic wave packets

Jochen Feldmann, T. Meier, G. von Plessen, Martín Koch, Ernst Otto Göbel, P. Thomas, Gerd Bacher, C. Hartmann, Heinz Schweizer, Wilfried Schäfer, Heinrich. Nickel

Published May 17, 1993• 90 citations
Publisher

Abstract

We report on the coherent dynamics of excitonic wave packets observed in transient four-wave mixing experiments on strained InGaAs/GaAs quantum-well structures. The excitonic noneigenstates are created by using laser pulses shorter than the electron round trip time within the exciton orbital. A characteristic temporal modulation of the diffracted signal is observed, which resembles the coherent dynamics of an electron wave packet in a hydrogen atom expected for the case of a simultaneous excitation of all bound and the lowest continuum states.

DOI
10.1103/physrevlett.70.3027

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We present an experimental and theoretical investigation of ultrafast transient four-wave mixing of GaAs/ ${\mathrm{Al}}_{\mathit{x}}$${\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.

Physical review. B, Condensed matter•Nov 15, 1996•38 citations
We report on the coherent dynamics of excitonic wave packets observed in transient four-wave mixing experiments on strained InGaAs/GaAs quantum-well structures. The excitonic noneigenstates are created by using laser pulses shorter than the electron round trip time within the exciton orbital. A characteristic temporal modulation of the diffracted signal is observed, which resembles the coherent dynamics of an electron wave packet in a hydrogen atom expected for the case of a simultaneous excitation of all bound and the lowest continuum states.
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.
The degenerate four-wave mixing technique in the self-diffraction geometry is employed to investigate a novel GaAs/AlAs quantum well microstructure. Time-integrated transient measurements are carried out to study the coherent dynamics of excitons in a GaAs quantum well with AlAs islands inserted at the center of the well (IIQW) in excitation densities from 6×109 to 1.5×1011 cm-2. The decay of the time-integrated self-diffracted signal shows slower dephasing for the IIQW compared to that of a normal quantum well (NQW) without island insertion. The dephasing rate is found to increase slightly in the IIQW, while it is found to increase sharply in the NQW with the excitation density. A deep beat with a period of 1.45 ps, which disappears for co-circular polarization configuration, is observed in the decay of the self-diffracted signal in the IIQW. The detection-energy-resolved measurement reveals that the modulation of the beat increases up to full depth at low detection energy with respect to the peak energy of the self-diffracted signal. The dependence on detection energy and on polarization configuration shows that the beat is a quantum beat due to biexcitonic effect, which is enhanced by localization due to island insertion.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.
We investigate the properties of coherent exciton states in GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$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 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.