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Physical review. B, Condensed matter

Coherent dynamics of continuum and exciton states studied by spectrally resolved fs four-wave mixing

Thomas Rappen, U. Peter, Martin Wegener, W. Schäfer

Published Aug 15, 1993• 49 citations
Publisher

Abstract

The coherent dynamics of continuum states and their interplay with excitons at the direct gap of germanium (T=1.8 K) is studied by femtosecond four-wave mixing. In order to unambiguously distinguish between the contribution of continuum states and excitons, we spectrally resolve the diffracted wave as a function of time delay for different excitation photon energies. For excitation many binding energies above the direct gap, the spectra exhibit two clearly separated maxima, one narrow line at the exciton and a much broader contribution of the continuum states. Surprisingly, the continuum contribution persists to longer time delays than the exciton. The experimental results are explained in the framework of the semiconductor Bloch equations.

DOI
10.1103/physrevb.48.4879

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The coherent dynamics of continuum states and their interplay with excitons at the direct gap of germanium (T=1.8 K) is studied by femtosecond four-wave mixing. In order to unambiguously distinguish between the contribution of continuum states and excitons, we spectrally resolve the diffracted wave as a function of time delay for different excitation photon energies. For excitation many binding energies above the direct gap, the spectra exhibit two clearly separated maxima, one narrow line at the exciton and a much broader contribution of the continuum states. Surprisingly, the continuum contribution persists to longer time delays than the exciton. The experimental results are explained in the framework of the semiconductor Bloch equations.
We investigate the coherent dynamics of excitons and continuum states at the direct gap of bulk germanium using femtosecond four-wave mixing. In particular, the dependence on the polarization of the incident beams is studied. Spectrally resolving the diffracted wave exposes a strikingly different behaviour of excitons and continuum states. We explain the different polarization dependences on the basis of the recently discussed density-induced dephasing. Applying a high magnetic field substantially changes the coherent response of the underlying system. This manifests itself in a significant modulation of the spectrally integrated four-wave mixing signal, which is interpreted as the time-resolved cyclotron motion of carriers.
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.
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.
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 present an experimental study of the coherent dynamics in quantum wells for the simultaneous excitation of Lorentzian excitons below the band edge and structured exciton Fano continua corresponding to higher-order subband transitions. Spectrally resolved transient four-wave mixing (FWM) experiments with 100 fs pulses were performed on a 500 \AA{} broad GaAs/${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ quantum well over a wide range of carrier densities. At lower carrier densities, the dephasing times of the different exciton transitions were determined from the width of the narrow resonances in the distinctly structured FWM spectra. These data demonstrate that the decay of the FWM signal from exciton Fano continua in the time-delay domain is not determined by dephasing at the lowest carrier densities. This is indicative of quantum interference which has its origin in many-body exciton-continuum coupling. At higher carrier densities, the FWM spectra are much less structured due to stronger dephasing, quantum interference effects lose their importance, and the structured exciton Fano continua show properties similar to unstructured continua without embedded exciton transitions.
The memory structure induced by coherent transitions to the exciton-exciton scattering continuum is shown to have significant influence on spectrally resolved four-wave-mixing signals even under selective excitation of 1s excitons. Comparisons between experiments and calculations that account nonperturbatively for these quantum kinetic Coulomb correlations demonstrate large compensations between mean-field contributions and transitions to the two-pair continuum. Experiments with different polarizations of the laser pulses show that two-pair continuum correlations are responsible for delay-time dependent shifts of the excitonic emission as well as for substantial deformations of the line shape.