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Physical Review Letters

Coherence of Four-Particle Correlations in Semiconductors

Peter Kner, Wilfried Schäfer, R. Lövenich, D. S. Chemla

Published Dec 14, 1998• 113 citations
Publisher

Abstract

We report direct investigations of the coherence of four-particle (exciton-exciton) correlations by ultrafast four-wave mixing experiments. We determine the sensitivity of the coherence of the four-particle correlations to temperature and excitation density, comparing it to the coherence of the two-particle correlations. We discuss our results in terms of numerical solutions of the general kinetic equations, treating the four-particle correlations in the second order Born approximation. We introduce a simple model deduced from these kinetic equations that provides an intuitive interpretation of our results.

DOI
10.1103/physrevlett.81.5386

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Physical review. B, Condensed matter•Jun 15, 1996•105 citations
We report direct investigations of the coherence of four-particle (exciton-exciton) correlations by ultrafast four-wave mixing experiments. We determine the sensitivity of the coherence of the four-particle correlations to temperature and excitation density, comparing it to the coherence of the two-particle correlations. We discuss our results in terms of numerical solutions of the general kinetic equations, treating the four-particle correlations in the second order Born approximation. We introduce a simple model deduced from these kinetic equations that provides an intuitive interpretation of our results.
Summary form only given. The nonlinear optical response in semiconductors has traditionally been treated in a mean field approximation at the 2-particle level. Recent work, in particular comparisons of four-wave mixing (FWM) with microscopic theory, have demonstrated the importance of 4-particle correlations. Such experiments, however, are not optimally sensitive to correlations at the 6-particle level. In order to probe such six-particle correlations we compare the results of six-wave mixing (SWM) measurements with a detailed microscopic theory based on the dynamics controlled truncation scheme (DCT).
Correlations due to biexcitons as well as to two-pair scattering states are direct manifestations of Coulomb quantum kinetics. Effects resulting from the memory structure of the corresponding contributions to the optical interband polarization are analyzed taking a ZnSe single-quantum well as model system. Our calculations are based on a microscopic density matrix description using the dynamics controlled truncation scheme for closing the hierarchy of higher-order density matrices. A detailed comparison between experiment and theory allows for the identification of numerous effects directly reflecting different aspects of pair-correlations. In particular, we demonstrate various influences of the two-pair scattering continuum on four-wave-mixing signals. Furthermore, we show that signals with a dynamically changing polarization sensitively monitor a competition between coherent parts of the dynamics and signal components induced by incoherent exciton densities. Surprisingly, the phase of these signals is found to be almost unaffected by the presence of incoherent densities. This result can be traced back to a compensation of the influences on the phases resulting from different incoherent parts of the dynamics. Six-particle correlations representing transitions from incoherent densities to two-pair correlations turn out to be indispensable for a proper description of this effect.© (2001) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
Ultrafast nonlinear optical spectroscopy is used to study the coherent dynamics of optically excited electron-hole pairs in semiconductors. Coulomb interaction implies that the optical inter-band transitions are dominated, at least at low temperatures, by excitonic effects. They are further enhanced in quantum confined lower-dimensional systems, where exciton and biexciton effects dominate the spectra even at room temperature. The coherent dynamics of excitons are at modest densities well described by the optical Bloch equations and a number of the dynamical effects known from atomic and molecular systems are found and studied in the exciton-biexciton system of semiconductors. At densities where strong exciton interactions, or many-body effects, become dominant, the semiconductor Bloch equations present a more rigorous treatment of the phenomena. Ultrafast degenerate four-wave mixing is used as a tool to study the coherent exciton dynamics, and the importance of performing transform limited spectroscopy is demonstrated throughout.
We present a numeric calculation of the exciton–exciton correlation for a one-dimensional semiconductor model with long-range Coulomb interactions, taking into account the effect of the exciton continuum. We use the obtained correlation functions to calculate the time integrated intensity of the four wave mixing signal. Changing the central frequency of the exciting pulses we observe changes in the profile and in the rise time of the time integrated signal for negative delays in qualitative agreement with experimental results. Our results show theoretically how the exciton continuum affects the coherence of four-particle correlations.
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.