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

arXiv:cond-mat/0307117 · Physical Review Letters

Infinite-Order Excitonic Bloch Equations for Asymmetric Nanostructures

Margaret Hawton, Marc M. Dignam

Published Dec 29, 2003• 22 citations
arXivHTMLPDF

Abstract

We present a new exciton-based formalism for calculating the coherent response of asymmetric semiconductor multiple quantum well structures to ultrashort optical pulses valid to infinite order in the optical field and including the self-generated intraband fields. We use these equations to calculate and explain the oscillations with time delay of peaks in the spectrally resolved degenerate four-wave mixing signals from biased semiconductor superlattices, obtaining good agreement with experiment.

DOI
10.1103/physrevlett.91.267402

Related papers

Influence of exciton-exciton interactions on the coherent optical response in GaAs quantum wells

K. Bott, O. Heller, D. Bennhardt +7 more

The degenerate-four-wave-mixing response of excitons in GaAs quantum wells is modeled using the optical Bloch equations including exciton-exciton interactions. The results display a strong dependence on the polarization of the excitation pulses. The model predicts intensity and polarization dependences of the time-integrated signal and characteristic temporal features of the time-resolved and time-integrated response in excellent agreement with observations.

Physical review. B, Condensed matter•Dec 15, 1993•192 citations

Coherent excitonic effects in quantum wells

Jagdeep Shah, D. S. KIM

Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.

Journal de Physique IV (Proceedings)•Oct 1, 1993•1 citation

Theoretische Beschreibung kohärenter optischer Nichtlinearitäten in Halbleiter-Quantenfilmen

Buck, Michael

In order to optimize opto-electronic applications of semiconductor nanostructures, a deep understanding of optical nonlinearities is essential.One fundamental method currently used within this field of research is ultrafast optical spectroscopy.This work presents a theoretical study of optical nonlinearities in semiconductor quantum wells in the coherent time regime.The theory is based on the equations of motion for the coherent exciton and biexciton transition amplitudes.These equations are derived using two different ways: Heisenberg equations of motion in combination with the dynamics-controlled truncation theory and alternatively the non-equilibrium Green´s function technique. For the coherent regime both approaches are equivalent and can be used to formulate a coupled set of equations for the coherent excitation dynamics that is correct up to the third order in the optical field.In contrast to the dynamics-controlled truncation theory the non-equilibrium Green´s function technique allows the inclusion of incoherent scattering processes into the description.The theory is evaluated to describe pump and probe as well as four-wave-mixing experiments with ZnSe quantum wells.Numerical calculations for the coherent control of the macroscopic polarization andthe dependence of transient four-wave-mixing on the light-polarization and intensity are both in good agreement with experiments.In order to correctly describe elevated excitation conditions for the latter investigation, the theory is self-consistently extended such that the included excitonic and biexcitonic nonlinearities contribute up to arbitrary order in the optical field.

•Jan 1, 2005•1 citation

Ultrafast coherent dynamics of excitons of higher-order subbands in semiconductor quantum wells

S. Arlt, U. Siegner, François Morier-Genoud +1 more

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.

Radiative Processes and Dephasing in Semiconductors•Jan 1, 1998•0 citations

Coherent Exciton and Biexciton Nonlinearities in Semiconductor Nanostructures: Effects of Disorder

W. Langbein, Paola Borri, J. M. Hvam

The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.

Materials science forum•Dec 1, 1998•5 citations

Femtosecond coherent fields induced by many-particle correlations in transient four-wave mixing

W. Schäfer, D. S. Kim, Jagdeep Shah +5 more

We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.

Physical review. B, Condensed matter•Jun 15, 1996•105 citations
We present a new exciton-based formalism for calculating the coherent response of asymmetric semiconductor multiple quantum well structures to ultrashort optical pulses valid to infinite order in the optical field and including the self-generated intraband fields. We use these equations to calculate and explain the oscillations with time delay of peaks in the spectrally resolved degenerate four-wave mixing signals from biased semiconductor superlattices, obtaining good agreement with experiment.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.
In order to optimize opto-electronic applications of semiconductor nanostructures, a deep understanding of optical nonlinearities is essential.One fundamental method currently used within this field of research is ultrafast optical spectroscopy.This work presents a theoretical study of optical nonlinearities in semiconductor quantum wells in the coherent time regime.The theory is based on the equations of motion for the coherent exciton and biexciton transition amplitudes.These equations are derived using two different ways: Heisenberg equations of motion in combination with the dynamics-controlled truncation theory and alternatively the non-equilibrium Green´s function technique. For the coherent regime both approaches are equivalent and can be used to formulate a coupled set of equations for the coherent excitation dynamics that is correct up to the third order in the optical field.In contrast to the dynamics-controlled truncation theory the non-equilibrium Green´s function technique allows the inclusion of incoherent scattering processes into the description.The theory is evaluated to describe pump and probe as well as four-wave-mixing experiments with ZnSe quantum wells.Numerical calculations for the coherent control of the macroscopic polarization andthe dependence of transient four-wave-mixing on the light-polarization and intensity are both in good agreement with experiments.In order to correctly describe elevated excitation conditions for the latter investigation, the theory is self-consistently extended such that the included excitonic and biexcitonic nonlinearities contribute up to arbitrary order in the optical field.
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.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
We present a unified microscopic approach to four-wave mixing (FWM) in semiconductors on an ultrashort time scale. The theory is valid for resonant excitation in the vicinity of the excitonic resonance and at low densities. The most important many-particle effects, i.e., static and dynamical exciton-exciton interaction as well as biexcitonic effects are incorporated. The internal fields resulting from these interaction processes give rise to pronounced many-particle effects in FWM signals. Our results explain the dependence of FWM signals on the polarization geometry, especially if biexcitons contribute. Time-resolved (TR) FWM experiments show that the diffraction of the interaction induced fields dominate the FWM signals completely. This dominance of the interaction induced field at low temperatures is true regardless of density, detuning, or polarization geometry. While spectrally resolved FWM (-FWM) shows biexcitonic or bound excitonic contributions under various experimental conditions, TR-FWM is always completely delayed, peaking roughly at the dephasing time after both beams passed through. \textcopyright{} 1996 The American Physical Society.