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Physical Review B

Non-Markovian nature of exciton-exciton scattering in a GaAs single quantum well observed by phase-locked laser pulses

Yoshihiro Ogawa, Hirokazu Tahara, F. Minami

Published Apr 23, 2013• 11 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.87.165305

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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.
Summary form only given. The optical properties of semiconductor quantum wells (QW) and, in particular, the coherent dynamics of excitons following resonant excitation with ultrafast laser pulses have attracted much attention in recent years. It is generally accepted that there is a transfer of coherence between the optical field and the QW that disappears in a characteristic time T/sub 2/ (picoseconds for GaAs) after the laser is turned off. However, the questions as to how the coherence is actually induced and that of the nature of the coherent state of the solid are poorly understood. In this work we address these points by re-examining the longstanding problem of the (classical vs. quantum) nature of the ubiquitous beats associated with the light-hole (LX) heavy-hole (HX) excitons, which are observed in transient optical experiments on QW. To this end, we consider the coherent behavior of excitons using the simplest albeit non-trivial model where they are treated as non-interacting bosons. Our results bear directly on studies for which nonlinear effects are not important and are not aimed directly at explaining the fourwave-mixing (FWM) experiments that dominate the field. Nevertheless, since nonlinear effects are, typically, weak compared with harmonic contributions, the free boson picture provides in all cases the correct lowest order wavefunction of the photoexcited solid.
We investigate the spectral properties of the excitonic nonlinear response in a GaAs quantum-well sample containing wells of different thicknesses. We observe both the heavy-hole biexciton and the light-hole biexciton in the transient four-wave mixing spectrum and estimate their binding energy dependence on well width. For moderate excitation densities the signal for negative delay at the heavy-hole exciton and biexciton resonances is due to two-photon transitions to the biexciton states through the exciton states. The temporal behavior of the transient four-wave mixing signal from the heavy-hole exciton resonance is strongly dependent on the spectral position of the laser. We show that this effect is due to interference phenomena and to excitation-induced dephasing.
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).
We demonstrate the presence of strong exciton-exciton correlations in GaAs-AlGaAs multiple quantum wells by using the polarization selection rules for four-wave mixing and a test that was originally designed to distinguish between quantum beats and polarization interference. We show that, when the four-wave-mixing signal is produced by two pulses that have the same circular polarization, dynamic beating behavior is observed at the heavy-hole-light-hole frequency that provides evidence of Coulomb-induced correlations that go beyond those expected from the semiconductor Bloch equations in the Hartree-Fock approximation and beyond the local field corrections used in simple phenomenological models. Moreover, this behavior cannot be explained by invoking biexcitonic effects. We demonstrate that this dynamic excitonic coupling can be explained in terms of a competition between quantum-beat-like and polarization-interference-like behavior, and we show that such behavior can be used to place quantitative limits on the coupling strength. In addition, we use a simple phenomenological model to show that excitation-induced-dephasing can produce such correlations.
Pulse time-of-flight measurements at the heavy exciton resonance in GaAs quantum wells reveal large pulse delays which are dependent on intensity and pulse spectral width. The measured pulse velocities are comparable to those seen in bulk GaAs and are as low as 6.7\ifmmode\times\else\texttimes\fi{}106{10}^{6}106cm${\mathrm{s}}^{\ensuremath{-}1}$. We obtain quantitative agreement with a simple theory based on hole burning observed in the inhomogeneous exciton line, and we show that the measurements are useful in estimating exciton damping, under certain conditions.