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Journal of Experimental and Theoretical Physics Letters

Collective state of interwell excitons in GaAs/AlGaAs double quantum wells under pulse resonance excitation

A. V. Larionov, Vladislav B. Timofeev, J. M. Hvam, K. Soerensen

Published Feb 1, 2002• 22 citations
Publisher

Abstract

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.

DOI
10.1134/1.1475723

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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.
Photoluminescence spectra of interwell excitons in double GaAs/AlGaAs quantum wells (n-i-n structures) have been investigated (an interwell exciton in these systems is an electron-hole pair spatially separated by a narrow AlAs barrier). Under resonance excitation by circularly polarized light, the luminescence line of interwell excitons exhibits a significant narrowing and a drastic increase in the degree of circular polarization of photoluminescence with increasing exciton concentration. It is found that the radiative recombination rate significantly increases under these conditions. This phenomenon is observed at temperatures lower than the critical point and can be interpreted in terms of the collective behavior of interwell excitons.
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 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.
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.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.
We study the coherent response of an optically dense exciton system in GaAs quantum wells (QWs). For this, we resonantly excite 1s1s1s heavy-hole excitons in the QWs at 8 K with subpicosecond laser pulses. The excitonic polarization is probed using time integrated (TI) degenerate four wave mixing (DFWM) measurements in self-diffraction geometry. The average power density (I1){(I}_{1})(I1​) of the leading laser pulse is systematically increased to large values, keeping that of the delayed pulse small and fixed. The dephasing rate of the excitonic coherent polarization (determined by the rate of decrease of the TI-DFWM signal with delay between the exciting pulses) attains saturation at large I1{I}_{1}I1​ after an initial rise at small I1.{I}_{1}.I1​. In comparison, the coherent polarization (as given by the DFWM signal at a fixed delay) increases initially with I1,{I}_{1},I1​, reaches a peak and then decreases at large I1.{I}_{1}.I1​.