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Physical Review Letters

Unusually slow temporal evolution of femtosecond four-wave-mixing signals in intrinsic GaAs quantum wells: Direct evidence for the dominance of interaction effects

Dai‐Sik Kim, Jagdeep Shah, Theo C. Damen, Wilfried Schäfer, F. Jahnke, Stefan Schmitt-Rink, Klaus Köhler

Published Nov 2, 1992• 188 citations
Publisher

Abstract

Four-wave-mixing signals from excitons in high-quality GaAs quantum wells show an unusually slow temporal evolution, in stark contrast to the behavior expected for a noninteracting two-level system. We show that Coulomb interaction effects, generally neglected in the analyses of four-wave-mixing experiments, dominate the signals by 2 orders of magnitude. Numerical calculations based on extended optical Bloch equations for semiconductors provide good qualitative agreement with the data.

DOI
10.1103/physrevlett.69.2725

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Four-wave-mixing signals from excitons in high-quality GaAs quantum wells show an unusually slow temporal evolution, in stark contrast to the behavior expected for a noninteracting two-level system. We show that Coulomb interaction effects, generally neglected in the analyses of four-wave-mixing experiments, dominate the signals by 2 orders of magnitude. Numerical calculations based on extended optical Bloch equations for semiconductors provide good qualitative agreement with the data.
Time-resolved four-wave-mixing experiments are usually interpreted in terms of noninteracting two-level systems in order to obtain information on the polarization dephasing time T2{\mathit{T}}_{2}T2​. Recent experiments involving excitonic resonances in semiconductor quantum wells (including results presented in this paper) show striking qualitative deviations from this simple picture. In particular, an exponential tail is observed at low excitation for negative time delays. At high excitation, the four-wave-mixing signal is found to evolve into two distinct temporal maxima. We demonstrate that the microscopic origin of this time dependence can be understood in terms of coherent exciton-exciton interactions. We show in fact that this behavior is more general and should be seen in numerous dense media where strong nonlinear interactions of polarizations occur. In addition to presenting rigorous numerical results, we analyze two simple situations in which such interactions exist: dielectric media with local-field effects and the anharmonic oscillator. We derive analytical expressions for their time-dependent four-wave-mixing response and discuss the physical origin of these new nonlinear-optical effects.
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 the properties of coherent exciton states in GaAs/Alx{\mathrm{Al}}_{\mathit{x}}Alx​${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As quantum wells using the four-wave-mixing technique with subpicosecond time resolution. In the first part of this work, we show that many-body interactions in a solid manifest themselves in a line shape of the four-wave-mixing signal that is substantially different from the predictions of the generally used simple two-level model. In particular, the coherent interaction of the quasiparticles leads to a signal at negative delay times, in agreement with recent theoretical predictions. In the second part, we report in detail about experiments where energetically close exciton transitions are excited coherently with a short laser pulse. The quantum or polarization interference leads to the observation of quantum beats in the decay of the diffracted signal. These results demonstrate that quantum-beat spectroscopy can be applied to study intrinsic excitations in solids.