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arXiv:cond-mat/9411118 · Physical review. B, Condensed matter

Four-wave mixing and terahertz emission from three-level systems in quantum wells: Effects of inhomogeneous broadening

Xuejun Zhu, Mark S. Hybertsen, P. B. Littlewood, Martin C. Nuss

Published Oct 15, 1994• 7 citations
arXivHTMLPDF

Abstract

Using a perturbation theory based on the density-matrix formulation, we study the nonlinear optical responses of a noninteracting three-level model system to consecutive coherent pulsed excitations, as realized in several recent experiments involving excitonic transitions in quantum wells. The terahertz emission, which is a second-order response, and the four-wave mixing signal, a third-order response, are calculated within the rotating-wave approximation, in the presence of detuning, dephasing, and inhomogeneous broadening. We study the quantum beats in the photon echo from transient four-wave mixing experiments of a three-level system. We find that the temporal profile of the photon echo signal in the four-wave mixing experiments depends very strongly on the amount of inhomogeneous broadening of the energy levels involved. Both the position and the intensity of the peaks exhibit a smooth evolution from strong quantum beats to a conventional photon echo as the inhomogeneous broadening increases. These features from our noninteracting model system are compared with a recent experiment, and found to account for a number of experimental observations.

DOI
10.1103/physrevb.50.11915

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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.
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Summary form only given.The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms are found to be important. First, the excitation-induced dephasing FWM signal (EID), which leads to a strong dependence of the signal on the angle between the linear input polarizations. The presence of the EID in the mainly homogeneously broadened sample (25 nm) is shown by the beating between EID and two-photon coherence (TPC) at the exciton for negative delay and co-linear polarized excitation. It vanishes for cross-polarized excitation, thus excluding the importance of local-field effects.
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.
The polarization dependence of the ultrafast nonlinear response of localized excitons in GaAs/AlGaAs quantum wells has been investigated by spectrally resolved, transient four-wave mixing. The role of the excitation-induced dephasing in the delay dependence of the signal is discussed in detail. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay.
A systematic theoretical and computational investigation of the microscopic factors which determine the phase of the signal field in time-resolved quasidegenerate three-pulse scattering experiments is presented. The third-order phase-matched response is obtained by density-matrix perturbation theory using a Green-function formalism for a system composed of two well-separated sets of closely spaced energy levels. Equations for calculating the electric field of four-wave-mixing signals generated by path-length delayed pulses are given. It is found that the phase of the signal field is determined by the excitation pulse phases, the dynamics of the nonlinear polarization decay, the product of four transition dipole matrix elements, and by a pulse-delay-dependent phase modulation at the frequency of the first dipole oscillation in the four-wave-mixing process. Analytic results for a two-level Bloch model show the phase shift from rapid nonlinear polarization decay. The product of dipole matrix elements is real and positive for three-level processes (bleached ground-state absorption and excited-state emission), but can be real and negative for some four-level Raman processes. The pulse-delay-dependent phase modulation treated here is closely related to the interferometric pulse-delay-dependent amplitude modulation observed in some collinear experiments, and plays a role in producing photon echos in inhomogeneously broadened samples. Numerical calculations of phase-resolved electric fields for finite duration pulses using a Brownian oscillator model appropriate for condensed-phase dynamics are presented. The ability of pulse-delay-dependent phase modulation to encode the frequency of the initially excited dipole onto the phase of the signal field can be exploited to examine energy-level connectivity, reveal correlations hidden under the inhomogeneous lineshape, and probe relaxation pathways in multilevel systems.