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Physical review. B, Condensed matter

Ultrafast dephasing of continuum transitions in bulk semiconductors

S. Arlt, U. Siegner, J. Kunde, François Morier-Genoud, Ursula Keller

Published Jun 15, 1999• 17 citations
Publisher

Abstract

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 ${\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}.$ 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 ${\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As},$ 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 ${\mathrm{Al}}_{0.06}{\mathrm{Ga}}_{0.94}\mathrm{As}$ dominate the FWM signal at negative time delays.

DOI
10.1103/physrevb.59.14860

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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.
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.
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.
Using laser pulses of duration comparable to semiconductor relaxation and dephasing times, the coherent phenomena common to two-level systems have been demonstrated in II-VI and III-V semiconductors. These light-matter interactions are characterized by electrons and holes in their initially excited states and/or a macroscopic polarization that persists after the excitation. A nonthermal carrier distribution was observed in bulk CdSe, demonstrating the extremely fast energy relaxation possible when carrier-LO-phonon scattering is included. Quantum-confined CdSe microcrystallites were then employed to limit the available decay avenues. The one and two-pair transitions were characterized, and using spectral hole-burning, energy relaxation was shown to be substantially slower than in bulk. Dipole dephasing remained very rapid. Persistent macroscopic polarization was demonstrated in semiconductors through pump and probe experiments conducted on time scales faster than the inverse linewidth of the exciton. In the first set of experiments, it was found that the exciton optical Stark shift deviates from that predicted by a steady-state theory. The shift is smaller than expected and lasts longer than the pump pulse. Both effects are explained by free evolution of the exciton's polarization. Transient exciton bleaching is observed and shown to be a result of adiabatic following. In a second study of coherent polarization, spectral oscillations at negative delay times were studied. Oscillations were measured in a wide variety of semiconductors, temporally preceding several different pump-probe phenomena. By comparison with a semiclassical theory, it was shown that spectral oscillations in the spectral region of the exciton are evidence of persistent exciton polarization. Oscillations in the band are due to four wave mixing of the pump and probe beams.
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.