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Physical Review A

Transient four-wave-mixing line shapes: Effects of excitation-induced dephasing

H. Wang, Kyle B. Ferrio, Duncan G. Steel, P. R. Berman, Y. Z. Hu, Rolf H. Binder, Stephan W. Koch

Published Mar 1, 1994• 112 citations
Publisher

Abstract

We describe the transient four-wave-mixing (FWM) response in systems where decay of the optically induced coherence depends on the excitation level of the system. Using modified optical Bloch equations, we show that excitation-induced dephasing due to phase-interrupting excited-state interactions qualitatively modifies the temporal behavior and polarization dependence of the FWM signal.

DOI
10.1103/physreva.49.r1551

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We describe the transient four-wave-mixing (FWM) response in systems where decay of the optically induced coherence depends on the excitation level of the system. Using modified optical Bloch equations, we show that excitation-induced dephasing due to phase-interrupting excited-state interactions qualitatively modifies the temporal behavior and polarization dependence of the FWM signal.
We numerically calculate the transient-four-wave-mixing (TFWM) response in systems that exhibit either a resonance frequency or a dephasing rate that depends on the level of excitation, which can occur in semiconductors or a dense atomic vapor. These effects change the intensity dependence of the TFWM signal, causing it to display noncubic behavior for significantly lower pulse areas and even a reduction in signal intensity for increasing pulse area. They also qualitatively change both the temporal behavior and spectrum of the TFWM signal in ways that cannot adequately be described in perturbation theory. For time-integrated TFWM, the saturation behavior is also found to depend on the delay between pulses. For comparison, the effects of local fields are also calculated as they produce similar effects. These results can help provide discrimination among the various phenomena.
Summary form only given. In an optically dense material, such as a semiconductor or a dense vapor, many-body interactions can dramatically modify the results of coherent experiments as compared to the dilute limit. The optical Bloch equations (OBE), which are appropriate in the dilute limit, must be modified to include many-body interactions. Such modified OBE (MOBE) are correct for a dense vapor and a phenomenological approximation for semiconductors, where a full treatment is based on the interacting electron-hole Hamiltonian. Previously, terms describing the local field correction (LFC) and excitation-induced dephasing (EID) have been added to the OBE to describe interactions. We show that an excitation-induced shift (EIS) is equally important. Perturbation calculations demonstrate that EIS gives rise to an additional signal in transient four-wave-mixing (TFWM), a common experiment for probing coherence. Comparison to numerical calculations shows that perturbation theory does not adequately describe either EIS or EID.
A transient four-wave-mixing signal is shown to arise from an excitation induced shift. In semiconductors, this signal can be comparable to or stronger than signals arising from saturation, local fields, or excitation induced dephasing. Calculations using modified optical Bloch equations show that multiple peaks in the transient four-wave-mixing spectrum are a signature of an excitation induced shift contributing to the signal. We observe this experimentally from a semiconductor multiple quantum well and confirm the presence of a shift directly using spectrally resolved differential transmission.
The polarization dependence of the ultrafast nonlinear response of localized excitons in GaAs/AlGaAs quantum wells has been investigated by spectrally resolved, transient four-wave mixing. The role of the excitation-induced dephasing in the delay dependence of the signal is discussed in detail. In particular, we show experimentally that the excitation-induced dephasing gives rise to a photon echo in inhomogeneous systems. We develop a simple analytical model for the delay dependence of the signal, which enables us to deduce the dephasing time from the four-wave mixing decay.
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.
Coherent transient spectroscopy of semiconductor nanostructures has become an active field of research in recent years. Most such experiments are analyzed in terms of a simple two-level model in which the effects of interaction and induced fields are ignored. We discuss two very different cases where inclusion of these generally-neglected effects leads to large and important modification in the temporal response of the system. In the first case, interactions between excitons strongly modify the temporal response of four-wave-mixing (FWM) signals from quantum wells. This is the temporal analog of well-known effects in the spectral domain, such as bleaching of the exciton absorption and bandgap renormalization. In the second case, the shape of a low-intensity pulse is severely distorted after transmission through a typical quantum well sample. Interferometric measurements show that reradiation of induced polarization is responsible for the distortion. The distortion depends strongly on the dephasing time and has important implications for all time-resolved measurements. 1.