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Physical review. B, Condensed matter

Coupling of exciton transitions associated with different quantum-well islands

Martín Koch, Jochen Feldmann, Ernst Otto Göbel, P. Thomas, Jagdeep Shah, Klaus Köhler

Published Oct 15, 1993• 38 citations
Publisher

Abstract

We show by means of time-resolved four-wave-mixing experiments that the simultaneous excitation of energetically distinct and inhomogeneously broadened exciton transitions associated with spatially separated quantum-well islands leads to a beating photon echo. This shows that the exciton transitions cannot be described by uncoupled two-level systems. We discuss bleaching, screening, and dipole-dipole interaction as possible coupling mechanisms.

DOI
10.1103/physrevb.48.11480

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Physical review. B, Condensed matter•Apr 15, 1995•61 citations
We show by means of time-resolved four-wave-mixing experiments that the simultaneous excitation of energetically distinct and inhomogeneously broadened exciton transitions associated with spatially separated quantum-well islands leads to a beating photon echo. This shows that the exciton transitions cannot be described by uncoupled two-level systems. We discuss bleaching, screening, and dipole-dipole interaction as possible coupling mechanisms.
We show that time-resolved quantum beat spectroscopy in the four-wave mixing (FWM) geometry is a unique tool to investigate the electronic multi-level system associated with spectrally adjacent excitonic resonances. We have studied heavy- and light-hole excitons, excitons associated with different and spatially separated quantum wells, and excitons associated with spatially separated growth islands within the same quantum well. Though the linear spectra are qualitatively similar in all three cases, the respective beating of the time-resolved FWM-signal shows a very different dynamic behaviour in each case. We discuss appropriate electronic multi-level schemes and show that exciton transitions within different quantum wells can be described by independent twolevel systems. In contrast, excitonic transitions associated with different and spatially separated growth islands having different quantum well thickness are not independent but coupled.
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.
We have performed time-integrated as well as time-resolved femtosecond degenerate four-wave-mixing measurements on inhomogeneously broadened (Zn,Cd)Se/ZnSe quantum-well structures. Potential fluctuations due to alloy disorder in the ternary wells give rise to localized quasi-zero-dimensional excitons and biexcitons. For time-integrated detection, they manifest themselves by distinct (disorder-renormalized) quantum beats. Time resolving these transients reveals a free-induction-decay-like emission nature of the biexciton in contrast to the photon-echo exciton contribution. Using a five-level scheme, containing both biexcitons and antibound two-exciton states, this striking emission-type change is explained by fluctuation and correlation effects upon the biexciton binding energy. A combination of time-resolved and time-integrated four-wave mixing is thus a powerful tool to gain information about the disorder in a given kind of quantum structure.
We have investigated, by fully-time-resolved degenerate four-wave mixing (FWM), excitonic coherence phenomena in single GaAs∕AlGaAs\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}GaAs∕AlGaAs quantum wells which are known to exhibit localization. A magnetic field (0−−12T)(0--12\phantom{\rule{0.3em}{0ex}}\mathrm{T})(0−−12T) was applied in Faraday geometry as a means of altering the nature of the excitonic transitions in a controlled manner. When the system is excited by a sequence of pulses tuned in resonance with the heavy-hole excitons, the predominant behavior observed at positive interpulse delays is beating in the FWM emission due to polarization interference between uncoupled excitons localized by monolayer islands. For negative interpulse delay the variation of beat phase with delay changes sign as the magnetic field is increased. In order to understand this feature, we modeled a coupled three-level system and included local field effects as a simple phenomenological approach to describing many-body terms. Comparison with experiments shows that with a larger magnetic field, the contribution to the signal from the coupled system reduces while that from two noninteracting two-level systems increases. We attribute this to the increased confinement of the excitons with field, leading to reduced wavefunction overlap, and hence reduced coupling.
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.
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.