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Physical review. B, Condensed matter

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

K. Bott, O. Heller, D. Bennhardt, Steven T. Cundiff, P. Thomas, E. J. Mayer, G. O. Smith, R. Eccleston, J. Kühl, Klaus Ploog

Published Dec 15, 1993• 192 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.48.17418

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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.
We report time-resolved degenerate four-wave-mixing experiments on a high-quality single GaAs quantum well. The signals for parallel and cross-polarized exciting pulses show pronounced quantum beats with different frequencies corresponding to the heavy/light-hole splitting and the biexciton binding energy, respectively. Comparison of the experimental data with solutions of the optical Bloch equations for a phenomenological model system shows that these features result from strong contributions of the biexcitonic state. The importance of biexcitons to the nonlinear coherent response of the two-dimension exciton is further confirmed by the frequency dependence of the time-integrated four-wave-mixing signal amplitudes measured for the two polarization geometries.
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.
We investigate the four-wave mixing response of semiconductor quantum wells having a predominantly inhomogeneous broadening of the exciton states. The influence of the biexcitons on the nonlinear emission, in proximity to the lowest exciton resonance, is studied. Using about 1 ps long pulses, we show that biexcitons are created for all excitation energies lying within the broadened exciton absorption line, and that their binding energy does not depend on the exciton energy. Reducing the temporal width of cross-linearly polarized incident laser fields to about 0.1 ps, we observe a drastic changeover from a prompt response to a photon echo, and quite interesting beating phenomena, visible in time-integrated as well as in time-resolved experiments, appear. Our observations compare well with the numerical solutions of the optical Bloch equations for a five-level scheme. The influence of the inhomogeneous broadening on the beating phenomena is discussed.
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.
We perform two beam time integrated (TI) degenerate four wave mixing (DFWM) measurements on 8~nm GaAs quantum wells (QW). Pulses from a Ti-Sapphire laser resonantly excite only 1s heavy hole excitons. The power density of the leading pulse (I1) is increased, keeping that of the delayed pulse fixed and relatively small. We measure the TI-DFWM signal at different delays as well as the DFWM spectra at a fixed delay, as I1 is increased. We find that the dephasing rate, after an initial increase with I1, becomes independent of I1 for large I1. The spectrally integrated DFWM signal, which probes the coherent polarization of the resonantly excited QWs, initially increases with I1, reaches a peak and then decreases as 1/(root)I1 at large I1. The results are compared with theoretical models of exciton coherence.