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

Europhysics Letters (EPL)

On the Theory of Femtosecond Photon Echoes from Band-to-Band Transitions in Semiconductors

V. L. Gurevich, Д. А. Паршин, Д. А. Паршин

Published Jun 15, 1990• 22 citations
Publisher

Abstract

A theory of femtosecond photon echo pulse decay in semiconductors is developed. The echo is due to band-to-band transitions produced by two successive pulses of coherent light. We propose that the decay is a result of the unscreened carrier-carrier interaction that brings about dephasing of the electron-hole wave function. We come to the conclusion that the time of dephasing is proportional to n -1/3 , where n is the carrier concentration.

DOI
10.1209/0295-5075/12/4/016

Related papers

Theory of femtosecond photon-echo decay in semiconductors

S. V. Gantsevich, V. L. Gurevich, Д. А. Паршин +1 more

We investigate a mechanism responsible for the observed very short times of the photon-echo decay (of the order of a few femtoseconds) in semiconductors. It is associated with the loss of phase memory as a result of the interaction of the interband mixed state with an unscreened random Coulomb potential of the photocarriers and/or charged impurities. A time characteristic of a system of interacting electrons is found. This is the time of phase breaking ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$, which we calculate within the eikonal approximation using diagrammatic techniques. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is shown to be typically much shorter than both the time of electron-electron collisions and the period of plasma oscillations. We demonstrate that the screening of Coulomb potential cannot be built up during this time. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is proportional to ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/\mathit{d}}$ (where n is the carrier concentration and d the dimensionality of a system), which is consistent with the experimental results. The derived law of echo decay of the form exp[-(\ensuremath{\tau}/${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$${)}^{\mathit{d}}$] agrees with the results of numerical simulation, although it does not agree with the existing results of physical experiment. We believe that such a disagreement is of a fundamental nature and manifests a basic need for further experimental and theoretical work.

Physical review. B, Condensed matter•Nov 15, 1995•2 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

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

Photon echo in semiconductors: a stochastic approach

W. Vogel, Frank Herzel, K. Henneberger

Femtosecond photon echos in semiconductors are studied on the basis of a stochastic description of the polarization decay. A satisfactory agreement with experimental results [ Phys. Rev. Lett.61, 1647 ( 1988)] is found with respect to the nonexponential decay of the echo energy as a function of the time delay between the laser pulses. Moreover, the shape of the echo is studied, and the detuning of the laser frequency with respect to the band edge is found to depend significantly on the shape of the light pulses.

Journal of the Optical Society of America B•Sep 1, 1991•1 citation

Many-body theory of Rabi flopping and photon echo in semiconductors

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

The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.

Quantum Electronics and Laser Science Conference•May 12, 1991•1 citation

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
A theory of femtosecond photon echo pulse decay in semiconductors is developed. The echo is due to band-to-band transitions produced by two successive pulses of coherent light. We propose that the decay is a result of the unscreened carrier-carrier interaction that brings about dephasing of the electron-hole wave function. We come to the conclusion that the time of dephasing is proportional to n -1/3 , where n is the carrier concentration.
We investigate a mechanism responsible for the observed very short times of the photon-echo decay (of the order of a few femtoseconds) in semiconductors. It is associated with the loss of phase memory as a result of the interaction of the interband mixed state with an unscreened random Coulomb potential of the photocarriers and/or charged impurities. A time characteristic of a system of interacting electrons is found. This is the time of phase breaking ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$, which we calculate within the eikonal approximation using diagrammatic techniques. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is shown to be typically much shorter than both the time of electron-electron collisions and the period of plasma oscillations. We demonstrate that the screening of Coulomb potential cannot be built up during this time. ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$ is proportional to ${\mathit{n}}^{\mathrm{\ensuremath{-}}1/\mathit{d}}$ (where n is the carrier concentration and d the dimensionality of a system), which is consistent with the experimental results. The derived law of echo decay of the form exp[-(\ensuremath{\tau}/${\mathrm{\ensuremath{\tau}}}_{\mathit{c}\mathit{p}\mathit{h}\mathit{i}}$)d{)}^{\mathit{d}})d] agrees with the results of numerical simulation, although it does not agree with the existing results of physical experiment. We believe that such a disagreement is of a fundamental nature and manifests a basic need for further experimental and theoretical work.
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.
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.
Femtosecond photon echos in semiconductors are studied on the basis of a stochastic description of the polarization decay. A satisfactory agreement with experimental results [ Phys. Rev. Lett.61, 1647 ( 1988)] is found with respect to the nonexponential decay of the echo energy as a function of the time delay between the laser pulses. Moreover, the shape of the echo is studied, and the detuning of the laser frequency with respect to the band edge is found to depend significantly on the shape of the light pulses.
The availability of femtosecond pulses in the optical-frequency regime allows the study of coherent effects in the interaction between semiconductors and light. Because the properties of the exciting pulses become important ingredients in spectroscopy, the theoretical analysis must treat the complete time dependence of the system. For this purpose we use the semiconductor Bloch equations (SBE),1-3 which are the coupled equations of motion for the interband polarization and the electron and hole populations for an interacting electron-hole system in the random-phase approximation. The equations describe the electron-hole Coulomb attraction leading to excitonic features; they contain phasespace filling and band-gap renormalization effects, as well as the dipole interaction with the applied light field.
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​.