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physica status solidi (b)

Four‐wave mixing from individual excitons: Intensity dependence and imaging

Jacek Kasprzak, W. Langbein

Published Mar 5, 2009• 7 citations
Publisher

Abstract

Abstract We use heterodyne spectral interferometry (HSI) to investigate the transient four‐wave mixing field (FWM) from an individual localized excitonic transition. FWM intensity and spectrum as well as the spatial resolution in FWM hyperspectral imaging are measured as function of excitation intensity. A third‐order non‐linear response of the FWM followed by saturation and the onset of a Rabi‐flop are observed with increasing intensity. The intensity dependence of the spectral response depends on the excitation pulse duration. For short pulses (∼0.2 ps), having a broad spectrum, a weak broadening of the emission line, similar to excitation induced dephasing (EID), is found. For long pulses (∼0.5 ps) instead, no signatures of EID are found, but individual multi‐excitonic transitions are observed. When using the FWM intensity as image contrast by spatially scanning a region of the sample surface, a spatial resolution beyond the diffraction limit is measured in the third‐order regime, while for higher intensities the FWM saturation deteriorates the spatial resolution. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200880583

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We present a novel heterodyne‐detected four‐wave mixing technique, which determines the third‐order nonlinear polarization in phase and amplitude by spectral interferometry. It allows us to measure the resonant transient four‐wave mixing of single localized excitons, both frequency and time‐resolved. In the signal, the strength of the coupling between two probed exciton transitions is directly observable. Applying a strong optical pump pulse, we observe optical Rabi oscillations of the exciton polarization. Observing decay of the third‐order polarization after the pump pulse, we can exclude the presence of signi£cant excitation‐induced dephasing.
The coherent emission from excitons corresponding to different subband transitions in a 500 Åbroad GaAs/AlGaAs quantum well is studied by spectrally resolved transient four-wave mixing (FWM). For the simultaneous excitation of several subband transitions, the dephasing times of the lowest exciton and higher- order exciton transitions are determined from the width of the resonances in the FWM spectrum. The decay of the spectrally integrated FWM signal as a function of the time delay between the excitation laser pulses does not reflect the dephasing times but is determined by the laser pulse width for multi-subband excitation. This is indicative of quantum interference between exciton and continuum transitions. Many-body Coulomb effects have to be included in a theoretical treatment of these experimental observations.
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Summary form only given.The coherent response of excitons in semiconductor nanostructures, as measured in four wave mixing (FWM) experiments, depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs-AlGaAs single quantum wells (SQW) of 4 nm to 25 nm well width. Two main mechanisms are found to be important. First, the excitation-induced dephasing FWM signal (EID), which leads to a strong dependence of the signal on the angle between the linear input polarizations. The presence of the EID in the mainly homogeneously broadened sample (25 nm) is shown by the beating between EID and two-photon coherence (TPC) at the exciton for negative delay and co-linear polarized excitation. It vanishes for cross-polarized excitation, thus excluding the importance of local-field effects.
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.
Abstract Four‐wave mixing (FWM) optical response from a sample containing a non‐homogeneously broadened ensemble of vertically stacked pairs of quantum dots is studied theoretically. The effects of collective interaction between the dots and their electromagnetic environment are analyzed. It is shown that the shape of the FWM echo is affected by the coupling between the two dots and, to some extent, by the statistics of the ensemble. In the time‐integrated signal, oscillations on picosecond delay time scale appear which lead to a reduction of the coherent response for coupled dots. For longer delays, the evolution is dominated by radiative decay, with the decay rate increasing from Γ to 2Γ(superradiance effect) as the coupling becomes stronger. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)