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Journal de Physique IV (Proceedings)

Quantum beats and polarization interference from excitons in quantum wells

Jochen Feldmann

Published Oct 1, 1993• 1 citation
Publisher

Abstract

We show that time-resolved quantum beat spectroscopy in the four-wave mixing (FWM) geometry is a unique tool to investigate the electronic multi-level system associated with spectrally adjacent excitonic resonances. We have studied heavy- and light-hole excitons, excitons associated with different and spatially separated quantum wells, and excitons associated with spatially separated growth islands within the same quantum well. Though the linear spectra are qualitatively similar in all three cases, the respective beating of the time-resolved FWM-signal shows a very different dynamic behaviour in each case. We discuss appropriate electronic multi-level schemes and show that exciton transitions within different quantum wells can be described by independent twolevel systems. In contrast, excitonic transitions associated with different and spatially separated growth islands having different quantum well thickness are not independent but coupled.

DOI
10.1051/jp4:1993540

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Physical review. B, Condensed matter•Oct 15, 1993•38 citations
We show that time-resolved quantum beat spectroscopy in the four-wave mixing (FWM) geometry is a unique tool to investigate the electronic multi-level system associated with spectrally adjacent excitonic resonances. We have studied heavy- and light-hole excitons, excitons associated with different and spatially separated quantum wells, and excitons associated with spatially separated growth islands within the same quantum well. Though the linear spectra are qualitatively similar in all three cases, the respective beating of the time-resolved FWM-signal shows a very different dynamic behaviour in each case. We discuss appropriate electronic multi-level schemes and show that exciton transitions within different quantum wells can be described by independent twolevel systems. In contrast, excitonic transitions associated with different and spatially separated growth islands having different quantum well thickness are not independent but coupled.
The nature of the beat modulations observed in nonlinear four-wave mixing in semiconductors is determined by spectral resolution of the time-integrated four-wave-mixing signals. Beats between close-lying bound-exciton resonances in CdSe are found to be described by macroscopic polarization interferences between two noninteracting two-level systems. Beats between heavy-hole excitons and light-hole excitons in GaAs quantum wells, on the other hand, are described by a three-level system, i.e., as a true quantum interference phenomenon.
In recent years, transient four-wave mixing (FWM) techniques have been used to investigate the dephasing times of non-equilibrium carriers in semiconductor heterostructures by monitoring the decay of the macroscopic polarization. Initially, this decay was measured by temporally-integrating the scattered FWM signal as a function of time delay between two (or more) pump pulses. More recently, the macroscopic polarization decay has been measured by time-resolving the FWM signal by cross correlating it with an ultrashort laser pulse via frequency up-conversion in a nonlinear crystal. When excitons with slightly different energies are excited, oscillations (or beats) have been observed both in the time-integrated FWM signal and in the time-resolved FWM signal. Such beats have been observed, for example, between light- and heavy-hole excitons and between excitons in wells of different widths. Both the spectral behavior1 of the time-integrated FWM signal and the temporal behavior2 of the time-resolved signal have been shown to allow the distinction between the polarization interference associated with two independent oscillators and the quantum beats associated with two coupled oscillators which share a common level. In addition, it has been demonstrated3 that the quantum beats produced by incident pulses with parallel polarizations are exactly out of phase (by π) with the beats produced by orthogonally polarized pulses. In each case1-3, the period and phase of the beats and the polarization of FWM signal were explained by using a six-level model, which excluded many-body effects, to describe the J=1/2 conduction and J=3/2 valence states. Within the last few months, however, it has been shown that a complete description of the polarization selection rules for the FWM signal requires excitation-induced dephasing4 or disorder-induced coupling of the σ + and σ – excitonic transitions5.
Summary form only given. Here, we use the polarization selection rules for four-wave mixing (FWM) and a test that was originally designed to distinguish between quantum beats and polarization interference to demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells. We show that when the four-wave-mixing signal is produced by two pulses having the same circular polarizations that quantum-beat-like behavior is observed. The latter observation is contrary to the predictions based on either the density matrix equations for two independent three-level systems (without many body effects) or the conventional semiconductor Bloch equations (SBE), both of which predict that polarization interference, but not quantum beats, should be observed. Consequently, these observations provide clear evidence for exciton-exciton correlations and evidence that those correlations go beyond those contained in the SBE. The procedure described here provides a simple effective test for such processes. Finally, we show that the quantum-beating-like behavior can be reproduced by including a density-dependent dephasing term (so-called excitation-induced dephasing, or EID) in the density matrix equations.
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.
Dual-channel spectral interferometry is used to measure the vectorial dynamics of the the four-wave-mixing signal from a GaAs-AlGaAs multiple quantum well when both heavy-and light-hole excitons are excited. The ellipticity, the orientation, and the sense of rotation of the polarization ellipse associated with this emission are observed to oscillate dramatically at the heavy-hole-light-hole quantum beat frequency. The qualitative nature of the beating can be described by a simple model based on the density matrix equations for two independent three-level systems without the inclusion of many body effects; however, these beats are superposed on a polarization that is dominated by many-body effects.