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International Conference on Ultrafast Phenomena

Biexcitonic effects in coherently controlled six-wave-mixing experiments on ZnSe quantum wells

Hans Georg Breunig, T. Voss, Ilja Rückmann, J. Gutowski

Published Jan 1, 2002• 0 citations
Publisher

Abstract

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.

DOI
10.1364/up.2002.wd2

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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 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 six-wave-mixing experiments on a ZnSe single quantum well are performed with different polarizations of the excitation pulses to enable or disable the creation of a biexcitonic polarization. A significant contribution of the biexcitonic polarization and other two-pair correlations is observed in the signal which is mainly modulated with the exciton transition frequency. A microscopic theory based on the dynamics controlled truncation scheme including six-point correlations is able to reproduce the experimental results.
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.
The coherent control of excitonic and biexcitonic polarization in pulse-transmission and four-wave-mixing (FWM) experiments is analysed with real time resolution. As a model system a ZnSe single quantum well is exclusively excited at the heavy-hole exciton and exciton–biexciton resonance. In pulse-transmission experiments the coherent control of excitonic polarization is shown for low excitation intensities. At elevated excitation intensities the dephasing time of the polarization is found to be strongly dependent on the relative phase of two phase-locked laser pulses which perform the coherent manipulation of the polarization. In FWM experiments the separate coherent control of the excitonic and biexcitonic FWM polarization is demonstrated which enables a coherent manipulation of the amplitude and phase of exciton–biexciton beats which are observed on the FWM polarization transients.
By use of an optical coherent-control technique we demonstrate and analyze the control of transitions involved in the generation of four-wave-mixing signals in a semiconductor quantum well for the two different four-wave-mixing directions and for different sequences of the excitation pulses. Results are presented for frequency- as well as for time-resolved signals. A doubling of the coherent switching frequency is found which occurs if the laser pulses performing the control process contribute quadratically to the wave-mixing signal. A direct comparison between experiment and microscopic theory reveals how the coherent-control process acts on the coherent polarization of the exciton-biexciton system in all different configurations. An additional interpretation of the experimental results based on a simplified few-level model is able to provide an intuitive understanding of the relevant processes which govern the coherent control of the excitonic and biexcitonic wave-mixing polarizations.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.