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IEEE Journal of Quantum Electronics

Heavy-hole and light-hole quantum beats in the polarization state of coherent emission from quantum wells

Arthur L. Smirl, Xi Chen, Osvaldo Buccafusca

Published Apr 1, 1999• 11 citations
Publisher

Abstract

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.

DOI
10.1109/3.753656

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Physical review. B, Condensed matter•Feb 15, 1995•13 citations
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.
Dual-channel spectral interferometry is used to measure the ellipticity, the orientation of the polarization ellipse, and the sense of rotation of the four-wave-mixing signal from a GaAs-AlGaAs multiple quantum well. Each parameter is observed to oscillate dramatically at the heavy-hole-light-hole quantum beat frequency. During each beat period (in the strong quantum beat regime), the ellipticity oscillates twice between linear and almost-circular polarization, the orientation of the polarization ellipse rotates through a complete 180 degrees , and the sense of rotation changes from left- to right-circular polarization.
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.
A dual-channel version of spectral interferometry is used to completely characterize the extremely weak ultrashort coherent four wave mixing (FWM) emission from multiple quantum wells (MQWs) by time resolving the polarization state, as well as the scalar amplitude and phase. The amplitudes and the phases of the x and y components of the coherent FWM emission are found to exhibit systematic (but distinct) variations with excitation fluence, time delay between the two incident pulses, detuning of the laser wavelength from the heavy hole (hh) exciton, and the orientation of the input polarizations. From these, a self consistent picture of the temporal dynamics of the amplitude, phase and polarization state is obtained that delineates the roles of many body effects, such as local field corrections, excitation-induced dephasing and biexcitons, in determining the excitonic dynamics.
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.
Shifts in the relative phases of quantum beats in the time-resolved four-wave-mixing signals from a GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As multiple quantum well are observed. The relative phases are shown to depend strongly on the intensities of the incident pulses as well as their detuning from the heavy-hole exciton. A simple coupled six-level model shows that the phases of the quantum beats are directly determined by many-body effects such as density-dependent dephasing and the local-field correction.