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physica status solidi (b)

Interferometric Four-Wave-Mixing Experiments on ZnSe Quantum-Well Structures

Hans Georg Breunig, T. Tr�per, I. R�ckmann, J. Gutowski, F. Jahnke

Published Jan 1, 2002• 9 citations
Publisher

Abstract

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.

DOI
10.1002/1521-3951(200201)229:2<621::aid-pssb621>3.0.co;2-z

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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.
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.
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.
Spectrally resolved and time-integrated degenerate four-wave mixing (FWM) experiments with ultra-short pulses have been used to investigate the relaxation times and coherent interactions of excitons in the Boltzmann and in the quantum kinetic regime in ZnSe single quantum wells.Three-pulse FWM experiments using 100 fs pulses in a 10 nm thick ZnSe/ZnMgSe single quantum well reveal nearly equal zero-density dephasing rates for coherences between + σ and - σ 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 + σ and + σ heavy-hole excitons.The different coherent nonlinear signals obtained in a three-beam FWM experiment are explained and reproduced by numerical calculations of the optical Bloch equations for a ten-level model including excitation induced dephasing (EID).Two-beam FWM experiments using 30 fs pulses on a 10 nm ZnSe quantum well reveal marked quantum beats and a pronounced non-exponential decay for delay times smaller ~500 fs.The pronounced peak at pulse overlap is attributed to rapid destructive interference of the created polarization and to spin dependent quantum kinetic effects caused by the transient formation of an electron-hole (eh) pair grating.The three-beam FWM trace shows a bi-exponential decay which is attributed to a nonlinear polarization that is caused by the interaction of polarization 3 k with both an exciton grating and an eh-pair grating.Model calculations using the OBEs of a two level system that includes ∑ -+
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.
Interaction-induced processes are studied using the third-order nonlinear polarization created in polarization-dependent four-wave-mixing experiments (FWM) on a ZnSe single quantum well. We discuss their influence by a comparison of the experimental FWM with calculations based on extended optical Bloch equations including local-field effects, excitation-induced dephasing, and biexciton formation. The investigations show that, for copolarized input fields, excitation-induced dephasing is the dominant FWM mechanism, followed by the conventional density-grating FWM process, biexcitonic contributions, and local-field effects. For cross-linear polarized input fields the excitation-induced dephasing mechanism is canceled so that the conventional density-grating FWM process and biexcitonic contributions are dominating.
We investigate the spectral and thermal dependence of an exciton resonant all-optical and phase coherent photorefractive effect in a ZnSe single quantum well by four-wave mixing using 90fs90\phantom{\rule{0.3em}{0ex}}\mathrm{fs}90fs pulses. The observed phase coherence is attributed to an exciton-induced formation of an electron grating within the quantum well. The diffracted signal exhibits an exponential decay that is equal to the exciton dephasing rate and it shows a pronounced suppression at the temporal overlap of incident pulses. With decreasing photon energy the diffracted signal traces reveal faster decay and the exciton transition is shifted towards lower energies indicating an increasing electron concentration within the quantum well. In temperature dependent measurements we observe a filling of the signal dip at pulse overlap and a transition from the photorefractive effect to a ${\ensuremath{\chi}}^{(3)}$ four-wave-mixing process below 35K35\phantom{\rule{0.3em}{0ex}}\mathrm{K}35K. Additional experiments using a cw pump laser are consistent with the proposed mechanism of the observed photorefractive effect. The phase coherent photorefractive signal is reproduced by a phenomenological model that is based on the optical Bloch equations for a five-level system.