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Journal of the Physical Society of Japan

Beating Structure on the Spectrally Resolved Four-Wave Mixing: Polarization Dependence

Teruya Ishihara, Yutaka Kadoya, Masamichi Yamanishi

Published Jul 15, 2000• 2 citations
Publisher

Abstract

We have performed spectrally resolved four-wave mixing measurements on inhomogeneously broadened GaAs/AlAs quantum-well structures. Under crosslinear polarization we observed a beating structure as a function of the delay time at higher energy region of the emission band with period of 0.95 ps. The beating was constructive at delaytime τ=0 ps. This behavior results from the interference between two biexciton intermediate states with different energies coupled to a common one-exciton state, as we show by a comparison with analytical model calculation of the double Feynman diagrams of the same type.

DOI
10.1143/jpsj.69.2349

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We have performed spectrally resolved four-wave mixing measurements on inhomogeneously broadened GaAs/AlAs quantum-well structures. Under crosslinear polarization we observed a beating structure as a function of the delay time at higher energy region of the emission band with period of 0.95 ps. The beating was constructive at delaytime τ=0 ps. This behavior results from the interference between two biexciton intermediate states with different energies coupled to a common one-exciton state, as we show by a comparison with analytical model calculation of the double Feynman diagrams of the same type.
The degenerate four-wave mixing technique in the self-diffraction geometry is employed to investigate a novel GaAs/AlAs quantum well microstructure. Time-integrated transient measurements are carried out to study the coherent dynamics of excitons in a GaAs quantum well with AlAs islands inserted at the center of the well (IIQW) in excitation densities from 6×109 to 1.5×1011 cm-2. The decay of the time-integrated self-diffracted signal shows slower dephasing for the IIQW compared to that of a normal quantum well (NQW) without island insertion. The dephasing rate is found to increase slightly in the IIQW, while it is found to increase sharply in the NQW with the excitation density. A deep beat with a period of 1.45 ps, which disappears for co-circular polarization configuration, is observed in the decay of the self-diffracted signal in the IIQW. The detection-energy-resolved measurement reveals that the modulation of the beat increases up to full depth at low detection energy with respect to the peak energy of the self-diffracted signal. The dependence on detection energy and on polarization configuration shows that the beat is a quantum beat due to biexcitonic effect, which is enhanced by localization due to island insertion.
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.
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.
We investigate the four-wave mixing response of semiconductor quantum wells having a predominantly inhomogeneous broadening of the exciton states. The influence of the biexcitons on the nonlinear emission, in proximity to the lowest exciton resonance, is studied. Using about 1 ps long pulses, we show that biexcitons are created for all excitation energies lying within the broadened exciton absorption line, and that their binding energy does not depend on the exciton energy. Reducing the temporal width of cross-linearly polarized incident laser fields to about 0.1 ps, we observe a drastic changeover from a prompt response to a photon echo, and quite interesting beating phenomena, visible in time-integrated as well as in time-resolved experiments, appear. Our observations compare well with the numerical solutions of the optical Bloch equations for a five-level scheme. The influence of the inhomogeneous broadening on the beating phenomena is discussed.
Current issues in the study of light-matter interactions are coherence and quantum interference. With ultrafast nonlinear spectroscopy such as transient four-wave mixing (TFWM) the imposed coherence on the optical excitations in e.g. GaAs multiple quantum wells has been studied. In this contribution, we study the influence of inhomogeneous broadening on quantum beats observed by spectrally resolved TFWM. In artificially grown semiconductor structures as e.g. quantum wells, inhomogeneities due to interface-disorder has, up till now, been inevitable. In the experiments, the light-hole exciton (lhx) and the heavy-hole exciton (hhx) in a 100 Å GaAs multiple quantum well are excited simultaneously with 150 fs pulses from a self mode-locked Ti:sapphire laser. The spectral profile is shown in the inset of Fig. 1.