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Physical review. B, Condensed matter

Temporally and spectrally resolved amplitude and phase of coherent four-wave-mixing emission from GaAs quantum wells

X. Chen, Wojciech J. Walecki, Osvaldo Buccafusca, David N. Fittinghoff, Arthur L. Smirl

Published Oct 15, 1997• 23 citations
Publisher

Abstract

We demonstrate that spectral interferometry can be used together with a well-characterized reference pulse to directly determine the spectral amplitude and spectral phase of coherent four-wave-mixing (FWM) emission from multiple quantum wells. The temporal amplitude and phase are then readily obtained by an inverse Fourier transformation. We illustrate that it is necessary to accurately determine the spectral phase, as well as the spectral amplitude, in order to correctly determine the temporal behavior. We subsequently use this technique to measure discontinuities in the temporal phase. Instabilities in the phase occur and phase jumps of $\ensuremath{\sim}\ensuremath{\pi}$ are produced when both the real and imaginary parts of the FWM field are zero. These jumps occur at the minima in the quantum beats, and this condition requires the excitation of approximately equal numbers of heavy- and light-hole excitons.

DOI
10.1103/physrevb.56.9738

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IEEE Journal of Quantum Electronics•Apr 1, 1999•11 citations
We demonstrate that spectral interferometry can be used together with a well-characterized reference pulse to directly determine the spectral amplitude and spectral phase of coherent four-wave-mixing (FWM) emission from multiple quantum wells. The temporal amplitude and phase are then readily obtained by an inverse Fourier transformation. We illustrate that it is necessary to accurately determine the spectral phase, as well as the spectral amplitude, in order to correctly determine the temporal behavior. We subsequently use this technique to measure discontinuities in the temporal phase. Instabilities in the phase occur and phase jumps of \ensuremath∼\ensuremathπ\ensuremath{\sim}\ensuremath{\pi}\ensuremath∼\ensuremathπ are produced when both the real and imaginary parts of the FWM field are zero. These jumps occur at the minima in the quantum beats, and this condition requires the excitation of approximately equal numbers of heavy- and light-hole excitons.
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.
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.
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.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.
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.