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Journal of Physics Condensed Matter

Interferences and coherent control of excitons in GaAs quantum wells

Joaquín Fernández-Rossier, C. Tejedor, Roberto D. Merlin

Published Jul 22, 1999• 3 citations
Publisher

Abstract

Coherent control and light-heavy-hole beats observed in transient optical experiments in GaAs quantum wells are discussed in terms of a free-boson model. The properties of the exactly calculated wavefunction of the photoexcited system lead to a reinterpretation of the beats as due to classical electromagnetic interference, in contrast to the widely used quantum description based on few-level representations.

DOI
10.1088/0953-8984/11/31/309

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Coherent control and light-heavy-hole beats observed in transient optical experiments in GaAs quantum wells are discussed in terms of a free-boson model. The properties of the exactly calculated wavefunction of the photoexcited system lead to a reinterpretation of the beats as due to classical electromagnetic interference, in contrast to the widely used quantum description based on few-level representations.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.
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.
Quantum beats of heavy and light holes in GaAs quantum wells are investigated in femtosecond time-resolved four-wave mixing and transmission experiments as a function of optical excitation energy. Under nonexcitonic excitation conditions, the four-wave mixing signal disappears due to the immediate loss of the interband coherence of continuum states. In the transmission experiment, the quantum beats are observed up to excess energies of 75 meV above the exciton resonances. The experimental data clearly demonstrate the coherence of continuum states in the valence band. Changes of the beat frequency with the excitation energy are due to the dispersion of the valence bands.
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.
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.