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Quantum Electronics and Laser Science Conference

Signatures of exciton correlations in the time-resolved vectorial polarization state of four-wave mixing signals from semiconductor quantum wells

I. Rumyantsev, Rolf H. Binder, Ryu Takayama, N. H. Kwong, Martin J. Stevens, A. L. Smirl

Published Jan 1, 2002• 0 citations
Publisher

Abstract

Summary form only given. The microscopic many-body theory applied to the time-resolved vectorial polarization state of the FWM signal documents two-exciton correlations. Under our experimental conditions, the biexciton dephasing rate is found to be much less than twice the exciton dephasing rate.
DOI
10.1109/qels.2002.1031303

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The studies described in this chapter convince the reader that time-resolved polarimetry is an extremely sensitive way to study many body effects. The vectorial dynamics contain useful information about many-body effects, quantum interference and optical anisotropies that would be difficult to obtain in any other way. The chapter begins with a brief review of some of the four-wave-mixing (FWM) techniques that have been most commonly used to measure the coherent emission from multiple quantum wells (MQWs). The ellipticity and the fraction of unpolarised light are both significantly smaller for the negative delay. These features provide additional tests for any proposed model that purports to describe coherent excitonic dynamics in MQWs. The chapter discusses the treatment of excitons in semiconductors as two-level systems, and follows with a detailed review of the solutions to the density matrix equations for two independent two-level systems, with an emphasis on the vectorial nature of the FWM emission from such systems.
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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.
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.