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Physical Review Letters

Quantum Coherence of Continuum States in the Valence Band of GaAs Quantum Wells

T. Dekorsy, A. M. T. Kim, G. C. Cho, S. Hunsche, Huib J. Bakker, H. Kurz, S. L. Chuang, Klaus Köhler

Published Sep 30, 1996• 20 citations
Publisher

Abstract

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.

DOI
10.1103/physrevlett.77.3045

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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.
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.
We describe a novel three-pulse degenerate four-wave mixing configuration that permits the direct observation of the coherence between the σ+ and the σ− exciton states in a GaAs quantum well excited in a two-photon process. It is found that the phase coherence between the two single heavy-hole exciton states decays with a time constant that is considerably longer than the dephasing time of the coherence between these states and the ground state (interband coherence). All the experimental data are well described by numerical solutions of the optical Bloch equations for a phenomenological multilevel model.
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.
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.
We investigate the properties of coherent exciton states in GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells using the four-wave-mixing technique with subpicosecond time resolution. In the first part of this work, we show that many-body interactions in a solid manifest themselves in a line shape of the four-wave-mixing signal that is substantially different from the predictions of the generally used simple two-level model. In particular, the coherent interaction of the quasiparticles leads to a signal at negative delay times, in agreement with recent theoretical predictions. In the second part, we report in detail about experiments where energetically close exciton transitions are excited coherently with a short laser pulse. The quantum or polarization interference leads to the observation of quantum beats in the decay of the diffracted signal. These results demonstrate that quantum-beat spectroscopy can be applied to study intrinsic excitations in solids.
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.