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Physical Review B

Coherent control of electron-phonon scattering and the dephasing process in GaAs multiple quantum wells

Yoshihiro Ogawa, F. Minami

Published Feb 2, 2007• 11 citations
Publisher

Abstract

We show the coherent control of the non-Markovian oscillation of exciton-folded acoustic phonon scattering in GaAs multiple quantum wells by using four-wave mixing measurements. The extent of non-Markovian scattering depends on the delay time ${t}_{{1}^{\ensuremath{'}}1}$ between the phase-locked pulses. The phenomenological dephasing time in the long-time (Markovian) region does not depend on the scattering. The dephasing process is suppressed when ${t}_{{1}^{\ensuremath{'}}1}$ corresponds to half the period of the non-Markovian oscillation. The dephasing suppression is the result of a fifth-order nonlinear optical effect (a six-wave mixing process).

DOI
10.1103/physrevb.75.073302

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We show the coherent control of the non-Markovian oscillation of exciton-folded acoustic phonon scattering in GaAs multiple quantum wells by using four-wave mixing measurements. The extent of non-Markovian scattering depends on the delay time t1\ensuremath′1{t}_{{1}^{\ensuremath{'}}1}t1\ensuremath′1​ between the phase-locked pulses. The phenomenological dephasing time in the long-time (Markovian) region does not depend on the scattering. The dephasing process is suppressed when t1\ensuremath′1{t}_{{1}^{\ensuremath{'}}1}t1\ensuremath′1​ corresponds to half the period of the non-Markovian oscillation. The dephasing suppression is the result of a fifth-order nonlinear optical effect (a six-wave mixing process).
Summary form only given. The coherence decay of optically excited electronic systems provides one of the most powerful tools to investigate interaction processes of excited states. In semiconductors, the optical coherence phenomena are usually investigated by nonlinear techniques such as four wave mixing (FWM), photon echo, or reflectivity experiments. Exciton-phonon, exciton-exciton, or exciton-free carriers scattering processes have been explored in recent years with these techniques. As demonstrated recently, a direct measurement of the optical dephasing time can be obtained through the temporal coherent control of electronic excitations. In these experiments, the emission following the excitation by an ultrashort optical pulse sequence, is detected in a non-specular direction (secondary emission). This provides an alternative approach to FWM techniques, which allows us to analyse the scattering processes either with phonons or due to mutual collisions. Using the coherent control technique monitored through the secondary emission (SE), we report on the coherent dynamics of excitons in bare quantum wells (QW) and compare it to that of exciton-polaritons in microcavity (MC) embedded quantum wells.
We report the non-Markovian nature of heavy hole-heavy hole and heavy hole-light hole exciton scattering in a GaAs single quantum well. The homogeneous width depends on the exciton population, which is controlled by the delay time of phase-locked pulses. This effect is explained on the basis of excitation-induced dephasing in Markovian approximation. For short times, the homogeneous width decreases and deviates from the Markovian behavior, due to the non-Markovian behavior of the exciton-exciton scattering. We analyze the homogeneous width by using a weakly interacting boson model including the non-Markovian effect. The correlation time of the exciton-exciton scattering is estimated as 0.43 ps.
We investigate the temporal evolution of the instantaneous frequency of ultrashort-pulse four-wave mixing in GaAs/Gax{\mathrm{Ga}}_{\mathit{x}}Gax​${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum-well structures. We find that the coherent light emitted by excitons exhibits a complex phase behavior which depends critically on the density of excitons and the central frequency of the exciting pulses. Depending on the excitation conditions, we observe nonlinear shifts of the instantaneous frequency within one ultrashort pulsed emission or quantum beats. In the latter case we determine that the beat \ensuremath{\pi}-phase shift is very fast, only 40% above the fundamental quantum limit. We also present elaborate numerical simulations of the experiments based on a six-band generalization of the semiconductor Bloch equations. This formalism takes into account Coulomb many-body interactions and Pauli exclusion. It reproduces the salient features of the experimental data. It fails to account for important details revealed by the very sensitive phase measurements. The discrepancies can be traced back to two approximations in the theory: the statical treatment of screening, and the Lorentzian description of dephasing. In both cases, this indicates the need for theoretical refinements requiring a microscopic description of Coulomb scattering and dephasing processes in a non-Markovian theory.
We investigate resonant time-resolved four-wave mixing on GaAs quantum wells at T=300KT=300\mathrm{K}T=300K and at elevated carrier densities using excitation with 11 fs optical pulses. The experiments are compared with non-Markovian quantum-kinetic calculations including carrier-carrier and carrier-LO-phonon scattering. A self-consistently determined two-time-dependent screened random-phase approximation Coulomb potential is used for the carrier-carrier scattering. In experiment and theory we find an unusual real-time response, which is far from an ideal photon echo. Surprisingly, we also find that the dependence of the decay time \ensuremath{\tau} of the four-wave-mixing signal versus the optically excited nonequilibrium electron-hole pair density neh{n}_{\mathrm{eh}}neh​ is quantitatively similar to the corresponding behavior of bulk GaAs. Thus both data sets can be fitted by the same form ${\ensuremath{\tau}}^{\ensuremath{-}1}={\ensuremath{\tau}}_{0}^{\ensuremath{-}1}{+cn}_{\mathrm{eh}}^{1/3}.$ This is not consistent with previous experimental work in a more limited range of carrier densities, which determined different behavior for quasi-two-dimensional (2D) and 3D, i.e., exponents of 0.3 and $0.55\ifmmode\pm\else\textpm\fi{}0.04,$ respectively.
The excitonic coherence in semiconductor quantum wells is measured by time-resolved speckle analysis and four-wave mixing. It is found that in the case of single GaAs quantum wells, the results of both methods are in agreement, and can be understood in the framework of an inhomogeneously broadened distribution of localized excitons which are subject to phonon-scattering and radiative recombination. The speckle analysis gives the additional distinction between recombination and pure dephasing processes. In multiple quantum wells, the radiative coupling between the quantum wells leads to a pronounced change of the observed dynamics. In the secondary emission, a strong coherent component with an oscillating time-structure is observed for small scattering angles. This is attributed to the beating of the radiative eigenstates of the stacked structure.