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physica status solidi (b)

Effects of Electronic Fourth-Order Correlations on the Pump-Probe Response of Semiconductors

U. Neukirch, S. R. Bolton, Lu Jeu Sham, D. S. Chemla

Published Sep 1, 2000• 3 citations
Publisher

Abstract

The pump-and-probe response of a ZnSe quantum well is investigated. In this particular sample the binding energy far exceeds both the exciton damping and the inhomogeneous broadening. A comparison between experimental data and model calculations shows that with co-circularly polarized beams the nonlinear mean-field contributions dominate those induced by four-particle correlations. In contrast, only the four-particle correlations contribute to the signal in counter-circular configuration. For this configuration, the exciton–biexciton interaction dominates the response for resonant excitation of the exciton. The occurrence of exciton–biexciton transitions leads to a renormalization of the period of coherent oscillations at negative pulse delay.

DOI
10.1002/1521-3951(200009)221:1<511::aid-pssb511>3.0.co;2-9

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Physical review. B, Condensed matter•Nov 7, 2002•11 citations
The pump-and-probe response of a ZnSe quantum well is investigated. In this particular sample the binding energy far exceeds both the exciton damping and the inhomogeneous broadening. A comparison between experimental data and model calculations shows that with co-circularly polarized beams the nonlinear mean-field contributions dominate those induced by four-particle correlations. In contrast, only the four-particle correlations contribute to the signal in counter-circular configuration. For this configuration, the exciton–biexciton interaction dominates the response for resonant excitation of the exciton. The occurrence of exciton–biexciton transitions leads to a renormalization of the period of coherent oscillations at negative pulse delay.
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.
Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical Bloch equations including local-field effects, excitation-induced dephasing, and biexciton formation. The investigations show that, for copolarized input fields, excitation-induced dephasing is the dominant FWM mechanism, followed by the conventional density-grating FWM process, biexcitonic contributions, and local-field effects. For cross-linear polarized input fields the excitation-induced dephasing mechanism is canceled so that the conventional density-grating FWM process and biexcitonic contributions are dominating.
A systematic analysis of excitonic and biexcitonic contributions to four-wave mixing in dependence on the polarization state and on the intensity of the exciting beams is presented for ZnSe/Zn1—xMgxSySe1—iiy quantum wells. The relative signals of excitons and biexcitons for different polarization configurations are discussed in terms of a microscopic density matrix model revealing excellent correspondence to the complex experimental data. In configurations which do not allow for a third-order contribution of the biexciton of zero angular momentum higher-order correlations are shown to become important already at densities as low as 1010 excitons cm—2/pulse.
The coherent interaction between excitons is revisited by examining the influence of coherent photo-excited excitons on the absorption spectra of ZnSe/ZnMgSSe multiple quantum wells for various polarization configurations. For purely resonant excitation at the heavy-hole exciton, a blueshift of the exciton absorption is found. This distinct blueshift shows a linear dependence on excitation fluence, but with different slopes for different polarization configurations. In the coherent regime the smallest shift is found for an orthogonal linear polarization of the pump and probe, noticeably smaller than the shift for same linear polarization. The strongest shift is found for the same circular polarization. Furthermore, we demonstrate experimentally that pump and probe and four-wave mixing spectra contain equivalent information about the shift and broadening of the exciton line. A linear correlation between the blueshift and the homogeneous linewidth is found in both pump and probe and four-wave mixing.
Four-wave-mixing signals from excitons under linear-circular polarized excitation exhibit an elliptical polarization, depending on both the pulse delay and the spectral position. Besides the resonances corresponding to excitons and exciton-biexciton transitions, a breakup of the exciton line is found reflecting the influence of correlations on the four-point level. An analysis accounting for the exciton density, the bound biexciton, and the exciton-exciton scattering continuum reveals that these features are not due to an antibound two-exciton state. Instead, they result from an interference of the correlated exciton continuum with the exciton density. In addition, the modeling shows that the signals ellipticity is highly sensitive to the influences of different correlations and, therefore, allows for a discrimination of their contributions.
Biexcitonic polarization excited in a ZnSe quantum well is coherently controlled with a pair of phase-locked laser pulses. The coherent control of this four-particle correlation is directly verified by observing a spectrally resolved four-wave-mixing signal in direction of the first order of diffraction of the pulse pair. By using polarization selection rules for the generation of biexcitons and changing the interpulse delay of the pulse pair the oscillations of the four-wave-mixing signal are studied at the energetic position of the excitonic as well as the biexcitonic resonance. The excitonic and biexcitonic signals exhibit a phase shift in dependence on the interpulse delay which clearly indicates the separate coherent control of the excitonic and biexcitonic polarization.