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Physical Review Letters

Raman Quantum Beats of Interacting Excitons

Kyle B. Ferrio, Duncan G. Steel

Published Jan 26, 1998• 77 citations
Publisher

Abstract

Quantum beats involving the light hole (lh) and heavy hole (hh) excitons in GaAs are observed using homodyne detection of the transient four-wave mixing response. Unlike the beats of earlier studies, these beats are detected in a geometry for which the effect would be forbidden in the absence of exciton interactions and arise from coherence induced between the lh and hh excitons. The beats demonstrate the existence of the Raman coherence due to interaction, and the decay of the coherence shows the correlation of exciton dephasing rates to be relatively unaffected by the interaction.

DOI
10.1103/physrevlett.80.786

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Quantum beats involving the light hole (lh) and heavy hole (hh) excitons in GaAs are observed using homodyne detection of the transient four-wave mixing response. Unlike the beats of earlier studies, these beats are detected in a geometry for which the effect would be forbidden in the absence of exciton interactions and arise from coherence induced between the lh and hh excitons. The beats demonstrate the existence of the Raman coherence due to interaction, and the decay of the coherence shows the correlation of exciton dephasing rates to be relatively unaffected by the interaction.
We demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells by using the polarization selection rules for four-wave mixing and a test that was originally designed to distinguish between quantum beats and polarization interference. We show that, when the four-wave-mixing signal is produced by two pulses that have the same circular polarization, dynamic beating behavior is observed at the heavy-hole-light-hole frequency that provides evidence of Coulomb-induced correlations that go beyond those expected from the semiconductor Bloch equations in the Hartree-Fock approximation and beyond the local field corrections used in simple phenomenological models. Moreover, this behavior cannot be explained by invoking biexcitonic effects. We demonstrate that this dynamic excitonic coupling can be explained in terms of a competition between quantum-beat-like and polarization-interference-like behavior, and we show that such behavior can be used to place quantitative limits on the coupling strength. In addition, we use a simple phenomenological model to show that excitation-induced-dephasing can produce such correlations.
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.
Three-beam time-integrated transient four-wave mixing (TFWM) is used to probe both light-hole (LH) and heavy-hole (HH) exciton coherences in weakly disordered GaAs quantum wells. The period of the quantum beats between the LH and the HH exciton coherences changes as a function of first-second pulse delay. A theoretical model for the TFWM signal, including exciton dephasing rates that vary with frequency across the inhomogeneous linewidth, reproduces the observations. The inclusion of inhomogeneous dephasing also improves the correspondence between theory and experiment when data as a function of both first-second and second-third pulse delays are simultaneously examined.
Quantum beats involving the light-hole and heavy-hole excitons in GaAs quantum wells are studied using both conventional and novel temporally gated differential detection techniques. The contributions of the exciton-exciton correlations are separated from those of the intervalence-band Raman coherence and the interband (population) coherence by monitoring the signal in the probe direction and by taking advantage of the polarization selection rules for the excitonic transitions. The results are shown to be in agreement with a theoretical analysis based on the dynamics-controlled truncation formalism.