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

Quantum Electronics and Laser Science Conference

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

Werner Hügel, M.F. Heinrich, M. U. Wehner, Martin Wegener

Published Jan 20, 2003• 0 citations
Publisher

Abstract

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.

DOI
10.1109/qels.1999.807346

Related papers

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

Werner Hügel, M. F. Heinrich, Martin Wegener +3 more

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 ${T}_{2}$.

Physical Review Letters•Oct 18, 1999•97 citations

Coherent optical polarization of bulk GaAs studied by femtosecond photon-echo spectroscopy

A. Lohner, Kai Rick, P. Leisching +5 more

The nonlinear polarization close to the band gap of GaAs is studied by spectrally and temporally resolved four-wave mixing. Excitonic and free carrier contributions both excited within the bandwidth of the 100 fs pulses are distinguished for the first time. The excitonic part dominates at carrier densities below ${10}^{16}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. At higher density, nonthermalized free carriers give rise to an additional component resonant to the pulse that shows a photon-echo-like time behavior. Monte Carlo simulations including the coherent polarization and the scattering dynamics of the carriers account for the data.

Physical Review Letters•Jul 5, 1993•80 citations

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

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

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

Femtosecond photon echo and four-wave mixing studies on GaAs/AlGaAs heterostructure at room temperature

Иванин Константин Валерьевич, Andrey V. Leontyev, Vladimir S. Lobkov +1 more

We report femtosecond photon echo and four-wave mixing measurements performed on GaAs/AlGaAs heterostructure at room temperature. In femtosecond photon echo experiment the dephasing time was obtained, found to vary between 40 and 55 fs depending on carrier density. The dependence showed a power-law behavior T 2 ∝ N -0.22 , which indicates that major phase coherence loss is due to screened Coulomb electron-electron interaction. Transient grating experiments yielded the electron diffusion coefficient value of 200 cm 2 /s and electron relaxation time equal to 3 ns.

Laser Physics Letters•Jun 1, 2010•10 citations
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 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 neh{n}_{\mathrm{eh}}neh​ 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 T2{T}_{2}T2​.
The nonlinear polarization close to the band gap of GaAs is studied by spectrally and temporally resolved four-wave mixing. Excitonic and free carrier contributions both excited within the bandwidth of the 100 fs pulses are distinguished for the first time. The excitonic part dominates at carrier densities below 1016{10}^{16}1016 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}3}$. At higher density, nonthermalized free carriers give rise to an additional component resonant to the pulse that shows a photon-echo-like time behavior. Monte Carlo simulations including the coherent polarization and the scattering dynamics of the carriers account for the data.
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.
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 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 report femtosecond photon echo and four-wave mixing measurements performed on GaAs/AlGaAs heterostructure at room temperature. In femtosecond photon echo experiment the dephasing time was obtained, found to vary between 40 and 55 fs depending on carrier density. The dependence showed a power-law behavior T 2 ∝ N -0.22 , which indicates that major phase coherence loss is due to screened Coulomb electron-electron interaction. Transient grating experiments yielded the electron diffusion coefficient value of 200 cm 2 /s and electron relaxation time equal to 3 ns.