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physica status solidi (a)

Coherent Oscillations in Multiwave Mixing Due to Higher-Order Coulomb Correlations

Hans Peter Wagner, H.-P. Tranitz, Matthias Reichelt, T. Meier, S. W. Koch

Published Apr 1, 2002• 0 citations
Publisher

Abstract

A three-beam configuration is used to investigate the spectrally resolved wave-mixing signal of a ZnSe single quantum well. The spectrum recorded in direction 2 k2–k1 shows coherent oscillations induced by a delayed third pulse with direction k3. Intensity and polarization-dependent measurements indicate that the signal is generated by a combination of four- and six-wave mixing. The origin of the oscillations can be explained qualitatively by a two-level model. The polarization-dependent experimental results require the treatment of many-body correlations and are well explained by microscopic calculations including four-particle correlations up to fifth order in the fields.

DOI
10.1002/1521-396x(200204)190:3<843::aid-pssa843>3.0.co;2-b

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A three-beam configuration is used to investigate the spectrally resolved wave-mixing signal of a ZnSe single quantum well. The spectrum recorded in direction 2 k2–k1 shows coherent oscillations induced by a delayed third pulse with direction k3. Intensity and polarization-dependent measurements indicate that the signal is generated by a combination of four- and six-wave mixing. The origin of the oscillations can be explained qualitatively by a two-level model. The polarization-dependent experimental results require the treatment of many-body correlations and are well explained by microscopic calculations including four-particle correlations up to fifth order in the fields.
Six-wave-mixing signals from a ZnSe quantum well are analyzed experimentally and with a microscopic density-matrix description using the dynamics-controlled-truncation scheme. For each physically distinct combination of polarizations of the exciting pulses, the spectrum of six-wave-mixing emission is measured as a function of time delay. The experimental results are compared with calculations performed at different levels of approximation. Although the leading order contributions to six-wave-mixing signals are of fifth order in the laser field, we show that there are significant signal components that are due to at least ${\ensuremath{\chi}}^{(7)}$ processes. The sensitivity of six-wave-mixing signals to high-order Coulomb correlations is demonstrated. Six-point density matrices are found to be indispensable for the interpretation of our experiments, while some details seem to indicate the involvement of even higher-order correlation functions. Furthermore, we find a remarkable dynamical decoupling of spectral signatures and the delay-time behavior after excitation with linearly polarized pulses.
We report interferometric four-wave-mixing (FWM) experiments on ZnSe quantum-well (QW) structures. By varying the phase relation of two phase-locked pulses in direction k1 (interferometric pulses) and using an additional pulse with wave vector k2 we observe an oscillating FWM signal in the direction 2 k2 — k1. This technique is specially suitable to investigate the influence of effects beyond third order with respect to the optical field, since these effects manifest themselves as higher integer harmonics in the observed FWM trace. We found a maximum influence of higher harmonics for overlapping interferometric pulses and for a delay time of roughly 1 ps of the third pulse. The experimental results are well reproduced by optical Bloch equations combined with a phenomenological density-dependent dephasing.
The manipulation of the coherent optical polarization in a quantum well with a pair of phase-locked laser pulses is investigated by using wave-mixing signals. The measurements are performed in four- and six-wave-mixing geometries with different polarization states of the excitation pulses. Even at moderate excitation densities, the signals are modulated by higher harmonics that correspond to high-order optical nonlinearities. A significant effect of higher Coulomb correlations on the coherent-control signals is demonstrated by comparing the experiments with calculations based on a microscopic density-matrix theory. The theoretical approach makes use of the dynamics-controlled truncation scheme. The corresponding numerical results are in good agreement with the experiment.
Biexcitonic polarization excited in a ZnSe quantum well is coherently controlled with a pair of phase-locked laser pulses. The coherent control of this four-particle correlation is directly verified by observing a spectrally resolved four-wave-mixing signal in direction of the first order of diffraction of the pulse pair. By using polarization selection rules for the generation of biexcitons and changing the interpulse delay of the pulse pair the oscillations of the four-wave-mixing signal are studied at the energetic position of the excitonic as well as the biexcitonic resonance. The excitonic and biexcitonic signals exhibit a phase shift in dependence on the interpulse delay which clearly indicates the separate coherent control of the excitonic and biexcitonic polarization.
Coherently controlled four-wave-mixing (FWM) measurements have turned out to be a very sensitive tool to investigate the microscopic origin of the nonlinear optical response of semiconductor quantum-well structures, in particular if excitons are excited [1-3]. The measured signal oscillates as a function of the phase difference of the two interferometric pulses and is modulated additionally by contributions that oscillate with integer multiples of the excitonic resonance frequency. The influence of these harmonics can be measured in background free directions, i.e., the first (FWM) or second (six-wave mixing, SWM) diffracted order in direction 2k2-k1 or 3k2-2k1, respectively. Their intensity is easily quantified by inspecting the corresponding Fourier transforms (FT). Here, we report on transient interferometric SWM measurements and the influence of biexcitons on the signal.
We investigate interband coherences as well as coherences between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ exciton states in a 10 nm thick ZnSe/ZnMgSe single quantum well by spectrally resolved three-pulse degenerate four-wave mixing using circularly polarized 100 fs pulses. Polarization and intensity dependent measurements are performed to identify the coherent processes responsible for the nonlinear signal into the ${\mathbf{k}}_{3}+{\mathbf{k}}_{2}\ensuremath{-}{\mathbf{k}}_{1}$ direction and to study the influence of Coulomb scattering on the dephasing rates. The experiments reveal nearly equal zero-density dephasing rates for coherences between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ heavy- and/or light-hole exciton states as compared to the dephasing rate of the interband coherence between these states and the ground state. The measurements also demonstrate that exciton--exciton scattering destroys the phase coherence between heavy- and light-hole excitons about three times more effectively than the coherence between ${\ensuremath{\sigma}}^{+}$ and ${\ensuremath{\sigma}}^{\ensuremath{-}}$ heavy-hole excitons. The characteristic features of the experimental results are explained and reproduced by numerical calculations of the optical Bloch equations for a ten-level model including excitation induced dephasing.