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Physical review. B, Condensed matter

Role of excitation-induced shift in the coherent optical response of semiconductors

Justin M. Shacklette, Steven T. Cundiff

Published Jul 17, 2002• 106 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.66.045309

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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.
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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 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.
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.
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.