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Applied Physics Letters

Photon echoes from two-dimensional excitons in GaAs-AlGaAs quantum wells

Lothar Schultheis, Michael D. Sturge, John Hegarty

Published Nov 1, 1985• 106 citations
Publisher

Abstract

We report photon echoes from two-dimensional (2D) excitons in a GaAs-AlGaAs quantum well structure at 2 K. We analyze our data with a theoretical model of the generation of photon echoes by pulses of finite length which includes phase relaxation during excitation. A line shape analysis yields the phase relaxation time of 2D excitons. We find that the phase coherence near the line center decays, together with the resonant population, within 4 ps, whereas well below line center the phase coherence is conserved for times up to 20 ps.

DOI
10.1063/1.95955

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Optics and Spectroscopy•Oct 1, 2008•4 citations
We report photon echoes from two-dimensional (2D) excitons in a GaAs-AlGaAs quantum well structure at 2 K. We analyze our data with a theoretical model of the generation of photon echoes by pulses of finite length which includes phase relaxation during excitation. A line shape analysis yields the phase relaxation time of 2D excitons. We find that the phase coherence near the line center decays, together with the resonant population, within 4 ps, whereas well below line center the phase coherence is conserved for times up to 20 ps.
The time evolution and kinetics of photoluminescence (PL) spectra of interwell excitons in double GaAs/AlGaAs quantum wells ( n-i-n structures) have been investigated under the pulse resonance excitation of intrawell 1sHH excitons using a pulsed tunable laser. It is found that the collective exciton phase arises with a time delay relative to the exciting pulse (several nanoseconds), which is due to density and temperature relaxation to the equilibrium values. The origination of the collective phase of interwell excitons is accompanied by a strong narrowing of the corresponding photoluminescence line (the line width is about 1.1 meV), a superlinear rise in its intensity, a long time in the change of the degree of circular polarization, a displacement of the PL spectrum toward lower energies (about 1.5 meV) in accordance with the filling of the lowest state with the exciton Bose condensate, and a significant increase in the radiative decay rate of the condensed phase. The collective exciton phase arises at temperatures T <6 K and interwell exciton densities n =3×10 10 cm −2 . Coherent properties of the collective phase of interwell excitons and experimental manifestations of this coherence are discussed.
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.
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.
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.
The mechanisms of exciton coherence relaxation in GaAs quantum wells in the linear mode have been experimentally investigated. An experimental technique has been developed for measuring the total phase relaxation rate, rates of reversible and temperature-irreversible excitonic phase relaxation, and the radiative decay rate Γ R of excitonic polarization. The experimental values of Γ R for a quantum well of specified thickness, obtained for a series of samples, have a spread not larger than 15%. This accuracy made it possible to estimate the shape of the dependence of Γ R on the well thickness L Z . It is experimentally found that Γ R is temperature-independent up to 80 K.