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Physical review. B, Condensed matter

Nonexponential photon echo decays from nanostructures: Strongly and weakly localized degenerate exciton states

John Erland, Jinwhan Kim, N. H. Bonadeo, Duncan G. Steel, D. Gammon, Douglas Scott Katzer

Published Sep 15, 1999• 12 citations
Publisher

Abstract

In a narrow GaAs quantum well, we resolve biexponential decays of optical coherences into decay-associated spectra identifying two distinct excitonic behaviors within the same inhomogeneously broadened absorption resonance. These excitonic states with overlapping spectra show different optical nonlinearities which allow us to identify them as noninteracting strongly localized excitonic states and weakly localized strongly interacting excitonic states.

DOI
10.1103/physrevb.60.r8497

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We report a comprehensive study of heavy-hole (HH) and light-hole (LH) excitons in a shallow GaAs/Al0.03Ga0.97As single quantum well (QW) using two-dimensional photoluminescence excitation (PLE) spectroscopy, reflectivity in Brewster geometry, and time-resolved four-wave mixing (FWM) with polarization-resolved photon echo (PE) detection. The PLE measurements reveal well-resolved HH and LH exciton states with minimal inhomogeneous broadening, while reflectivity spectra indicate strong light–matter coupling and narrow exciton linewidths, reflecting the high structural quality of the QW. FWM experiments demonstrate two-pulse photon echoes with coherence times of T2≈39.5 ps for HH and T2≈16.2 ps for LH excitons. Polarization-resolved PE confirms that the observed signals originate from pure three-level excitonic systems without contributions from trions or donor-bound excitons. Compared to conventional GaAs/Al0.3Ga0.7As QWs, the shallow QW exhibits reduced HH-LH splitting, enhanced optical homogeneity, and robustness against above-barrier illumination, making it a promising platform for coherent optical control and information photonics applications.

Photonics•Dec 26, 2025•1 citation
In a narrow GaAs quantum well, we resolve biexponential decays of optical coherences into decay-associated spectra identifying two distinct excitonic behaviors within the same inhomogeneously broadened absorption resonance. These excitonic states with overlapping spectra show different optical nonlinearities which allow us to identify them as noninteracting strongly localized excitonic states and weakly localized strongly interacting excitonic states.
Recent experimental and theoretical work suggests that excitons in GaAs/AlGaAs multiple quantum wells may be localized by disorder, or delocalized with Bloch-type wavefunctions1. At low temperature, localized excitons are expected to be characterized by spectral diffusion and by long optical coherence times, while delocalized excitons have short coherence times and exhibit spatial mobility2. The short optical coherence time associated with delocalized excitons results in a linear absorption profile that is primarily homogeneously broadened, while the disorder associated with localized excitons leads to an inhomogeneously broadened profile. In this work, we investigate the energy and phase relaxation of HH1 excitons in GaAs/AlGaAs MQW's at low temperature, and provide evidence that, dependent on the exciton density, both localized and delocalized excitons contribute to the nonlinear optical response.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
Summary form only given.Much recent progress has been made in the understanding of the optical response of low dimensional semiconductors. However, additional complications of strong localization and their effects on dynamics and the coherent optical response remain unresolved. Using a highly disordered GaAs single quantum well (width 42 /spl Aring/), we report the nonlinear signal in a self-diffracted transient four-wave mixing (FWM) experiment extending over more than three decades in amplitude as a function of pulse delay.
Optical coherence time and nonlinear optical response of excitons localized to quantum dots in a GaAs/AlGaAs single quantum well are investigated by the three-pulse photon echo technique. At low temperature, the optical coherence time is estimated to be 1.8 ns from the decay curve of the photon echo signal. The decay profile for short time delay shows the strong dependence on the input pulse area of the third pulse. Rabi oscillations are also observed. The oscillations exhibit nonlinear behavior, which is affected by the pre-excited polarization. Such behavior can be qualitatively explained by the local field effect due to the exciton-exciton interaction between the excitons.
This work presents new results of experimental studies of exciton relaxation in GaAs/AlGaAs multiple quantum well materials, using transient nonlinear laser spectroscopy techniques. In the low excitation regime, effective optical Bloch equations similar to the density matrix formalism of a two-level system describe the response. Solutions of these equations appropriate for three-pulse scattering studies are presented, along with a discussion of new experimental techniques used in this work. Non-ideal conditions present in the molecular beam epitaxy growth process introduce monolayer fluctuations in the quantum well thickness, leading to inhomogeneous broadening and exciton localization at sites of minimum energy. Localized excitons are separated in energy from extended, quasi-delocalized states by the mobility edge. Studies of localized exciton relaxation indicate that these excitons relax on a much slower timescale than delocalized excitons. The temperature dependence of the localized exciton relaxation rate shows that above 15K, the excitons are thermally activated to extended states above the mobility edge. Below 15K the excitons relax by phonon assisted migration between localization sites. For temperatures above 5K, and for exciton energies greater than 1 meV below line center, an extra dephasing mechanism characterizes the exciton relaxation. The inhomogeneous broadening of the exciton leads to the emission of stimulated photon echoes in the experimental geometry used in this work. The time-resolved emission demonstrates the stimulated photon echo nature at low excitation densities. At higher excitation densities, the decay dynamics is more complex. The time-resolved emission shows the presence of a stimulated photon echo and a free polarization decay. This unusual result suggests that both a homogeneous and an inhomogeneous exciton distribution comprise the exciton resonance. Exciton relaxation at low excitation densities represents the interaction of the exciton with the lattice. At higher excitation densities, exciton-exciton and exciton-free carrier interactions modify the relaxation rates. The dependence of the exciton relaxation rate on excitation density shows that many-body effects play an important role in the exciton physics. Free carrier interactions are more efficient at increasing the exciton relaxation rate; both types of interactions are more important in quantum well systems than in bulk materials.
We report a comprehensive study of heavy-hole (HH) and light-hole (LH) excitons in a shallow GaAs/Al0.03Ga0.97As single quantum well (QW) using two-dimensional photoluminescence excitation (PLE) spectroscopy, reflectivity in Brewster geometry, and time-resolved four-wave mixing (FWM) with polarization-resolved photon echo (PE) detection. The PLE measurements reveal well-resolved HH and LH exciton states with minimal inhomogeneous broadening, while reflectivity spectra indicate strong light–matter coupling and narrow exciton linewidths, reflecting the high structural quality of the QW. FWM experiments demonstrate two-pulse photon echoes with coherence times of T2≈39.5 ps for HH and T2≈16.2 ps for LH excitons. Polarization-resolved PE confirms that the observed signals originate from pure three-level excitonic systems without contributions from trions or donor-bound excitons. Compared to conventional GaAs/Al0.3Ga0.7As QWs, the shallow QW exhibits reduced HH-LH splitting, enhanced optical homogeneity, and robustness against above-barrier illumination, making it a promising platform for coherent optical control and information photonics applications.