Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review Letters

Photon Echoes from Semiconductor Band-to-Band Continuum Transitions in the Regime of Coulomb Quantum Kinetics

Werner Hügel, M. F. Heinrich, Martin Wegener, Q. T. Vu, L. Bányai, H. Haug

Published Oct 18, 1999• 97 citations
Publisher

Abstract

We show that the coherent response of semiconductor band-to-band continuum transitions at room temperature, excited by 11 fs pulses at elevated carrier densities, deviates substantially from that expected for an ideal photon echo. A microscopic non-Markovian quantum kinetic theory of both electron-electron and electron-LO-phonon scattering reproduces these unusual experimental observations qualitatively and, furthermore, the famous scaling of the decay time $\ensuremath{\tau}$ with carrier density ${n}_{\mathrm{eh}}$ according to ${\ensuremath{\tau}}^{\ensuremath{-}1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}$ quantitatively. $\ensuremath{\tau}$, however, cannot be associated with a single unique phase relaxation time ${T}_{2}$.

DOI
10.1103/physrevlett.83.3313

Related papers

Quantum-kinetic dephasing in resonantly excited semiconductor quantum wells

B. Mieck, H. Haug, Werner Hügel +2 more

We investigate resonant time-resolved four-wave mixing on GaAs quantum wells at $T=300\mathrm{K}$ 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 ${n}_{\mathrm{eh}}$ 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.

Physical review. B, Condensed matter•Jul 15, 2000•36 citations

Photon echoes from band-to-band transitions in semiconductors excited with 10-fs pulses

Werner Hügel, M.F. Heinrich, M. U. Wehner +1 more

Summary form only given. Even one decade after the pioneering photon echo experiments by Shank et al. (1988,1991) in which GaAs was investigated at room temperature using /spl ap/10 fs optical pulses, not a single experiment has actually shown directly that the coherent real-time response of semiconductor band-to-band transitions under these conditions is a photon echo indeed. Recent experiments with /spl ap/10 fs pulses exciting GaAs at low temperatures have explicitly shown that the response is not a photon echo for low excitation densities (/spl ap/10/sup 15/ cm/sup -3/). From these experiments it has also become clear that the coherent response after excitation with 10 fs pulses is distinctly different from that after excitation with 100 fs pulses. We investigate the coherent real-time response at elevated carrier densities using transient four-wave mixing and an up-conversion scheme with a time resolution of 5 fs. We focus on approximately resonant excitation (50 meV above gap) of a 0.6 /spl mu/m thin film of bulk GaAs at T=300 K.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Femtosecond Photon Echoes from Band-to-Band Transitions in GaAs

P. C. Becker, H. L. Fragnito, C. H. Brito Cruz +4 more

We report the first observation of femtosecond photon echoes from the band-to-band transitions in a bulk semiconductor. The time decay of the echo, found to vary from 3.5 to 11 fs, has allowed us to determine the polarization dephasing rate in GaAs. This rate was found to depend on the carrier density in the experimental range covered, 1.5\ifmmode\times\else\texttimes\fi{}${10}^{17}$ to 7\ifmmode\times\else\texttimes\fi{}${10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, indicating the dominance of carrier-carrier scattering as the principal dephasing mechanism. The observed functional dependence of the dephasing rate on the carrier density has yielded previously unavailable information on Coulomb screening in a nonequilibrium carrier distribution.

Physical Review Letters•Oct 3, 1988•450 citations

Ultrafast dephasing of continuum transitions in bulk semiconductors

S. Arlt, U. Siegner, J. Kunde +2 more

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.

Physical review. B, Condensed matter•Jun 15, 1999•17 citations

Ultrafast dephasing of continuum transitions in GaAs and AlGaAs

S. Arlt, U. Siegner, J. Kunde +2 more

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.

Quantum Electronics and Laser Science Conference•Jan 20, 2003•0 citations

Theory of the semiconductor photon echo

Markus Lindberg, Rolf H. Binder, Stephan W. Koch

The semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.

Physical Review A•Feb 1, 1992•212 citations
We show that the coherent response of semiconductor band-to-band continuum transitions at room temperature, excited by 11 fs pulses at elevated carrier densities, deviates substantially from that expected for an ideal photon echo. A microscopic non-Markovian quantum kinetic theory of both electron-electron and electron-LO-phonon scattering reproduces these unusual experimental observations qualitatively and, furthermore, the famous scaling of the decay time \ensuremathτ\ensuremath{\tau}\ensuremathτ with carrier density neh{n}_{\mathrm{eh}}neh​ according to \ensuremathτ\ensuremath−1=\ensuremathτ0\ensuremath−1+cneh1/3{\ensuremath{\tau}}^{\ensuremath{-}1}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}{\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}\ensuremathτ\ensuremath−1=\ensuremathτ0\ensuremath−1​+cneh1/3​ quantitatively. \ensuremathτ\ensuremath{\tau}\ensuremathτ, however, cannot be associated with a single unique phase relaxation time T2{T}_{2}T2​.
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.
Summary form only given. Even one decade after the pioneering photon echo experiments by Shank et al. (1988,1991) in which GaAs was investigated at room temperature using /spl ap/10 fs optical pulses, not a single experiment has actually shown directly that the coherent real-time response of semiconductor band-to-band transitions under these conditions is a photon echo indeed. Recent experiments with /spl ap/10 fs pulses exciting GaAs at low temperatures have explicitly shown that the response is not a photon echo for low excitation densities (/spl ap/10/sup 15/ cm/sup -3/). From these experiments it has also become clear that the coherent response after excitation with 10 fs pulses is distinctly different from that after excitation with 100 fs pulses. We investigate the coherent real-time response at elevated carrier densities using transient four-wave mixing and an up-conversion scheme with a time resolution of 5 fs. We focus on approximately resonant excitation (50 meV above gap) of a 0.6 /spl mu/m thin film of bulk GaAs at T=300 K.
We report the first observation of femtosecond photon echoes from the band-to-band transitions in a bulk semiconductor. The time decay of the echo, found to vary from 3.5 to 11 fs, has allowed us to determine the polarization dephasing rate in GaAs. This rate was found to depend on the carrier density in the experimental range covered, 1.5\ifmmode\times\else\texttimes\fi{}1017{10}^{17}1017 to 7\ifmmode\times\else\texttimes\fi{}1018{10}^{18}1018 ${\mathrm{cm}}^{\ensuremath{-}3}$, indicating the dominance of carrier-carrier scattering as the principal dephasing mechanism. The observed functional dependence of the dephasing rate on the carrier density has yielded previously unavailable information on Coulomb screening in a nonequilibrium carrier distribution.
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.
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 semiconductor Bloch equations are solved numerically for a two-pulse photon-echo configuration. The time-dependent diffracted signal is computed and the significance of many-body effects, carrier relaxation, and dephasing is investigated in detail. Assuming femtosecond-pulse excitation at various intensities and frequencies, distinctly different results are obtained if the exciton or the continuum electron-hole-pair states are excited. It is shown that pure exciton excitation produces a free-induction decay signal and no photon echo. An echo signal is obtained only if continuum states are excited either directly by choosing the central pulse frequencies appropriately or if the band-gap renormalization is sufficiently strong to shift continuum states into resonance. A continuous transition between free-induction decay and photon-echo signal is obtained with increasing excitation amplitude. A perturbative analytical analysis of the equations allows one to identify the role of the many-body effects in producing the different features.