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Physical Review B

Coherent control of the exciton and exciton-biexciton transitions in the generation of nonlinear wave-mixing signals in a semiconductor quantum well

T. Voss, Ilja Rückmann, J. Gutowski, V. M. Axt, T. Kühn

Published Mar 9, 2006• 31 citations
Publisher

Abstract

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.

DOI
10.1103/physrevb.73.115311

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Physical review. B, Condensed matter•Nov 7, 2002•11 citations
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.
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.
Abstract In experiments and simulations based on a microscopic theory the optical coherent control of exciton–biexciton beats in coherent four‐wave‐mixing signals from a semiconductor quantum well is demonstrated. It is found that a reduction of the beat amplitude for one four‐wave‐mixing direction may at the same time coincide with a large beat amplitude for the other direction. The results can be understood by considering that at least two‐photon processes are required to coherently excite biexcitonic transitions which are responsible for the occurrence of the beat structure in the four‐wave‐mixing signals. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Systematic measurements and microscopic simulations were performed to study the optical coherent control of the exciton‐biexciton systems in a ZnSe quantum well. Our results show that the spectral components in the four‐wave mixing signal at the exciton and the exciton‐biexciton transition, respectively, can be separately controlled in the coherent regime. This separate control also results in different beat structures on the real‐time transients of the nonlinear wave‐mixing polarization. With respect to all important features experiment and simulation are in excellent agreement.
The optical coherent-control technique is used to study biexcitonic effects in the four-wave-mixing signal of a ZnSe single quantum well. The signal is analyzed in both directions 2k1 − k2 and 2k2 − k1 which are not equivalent if a pulse pair is applied from direction k1 to achieve coherent control of the induced polarization. It is shown that the coherent control enables a selective enhancement or suppression of the contribution at the exciton and biexciton resonance to the signal, respectively, but only for certain sequences of the excitation pulses. Further, the suppression of exciton-biexciton beats in the signal as a function of tdel by a selective destruction of the biexciton polarization is demonstrated.
The paper presents a description of two-pair correlations in an electron-hole system in laser-excited direct-gap semiconductors in terms of the exciton-boson formalism. The dependence of the states of quasi-particles on their angular momentum orientation is properly taken into account following group theory rules. It is shown for the example of heavy hole excitons in GaAs quantum wells that Coulomb two-exciton correlations include effective repulsion between excitons with nonzero total momenta and effective attraction between excitons with zero total momenta. They generate exciton and biexciton nonlinearities, respectively, in the exciton-biexciton system. The Heisenberg equations of motion derived are applied to four-wave mixing in the coherent mode. Two components of Coulomb two-exciton correlations were found to generate coherent four-wave mixing either separately, one at the cocircular and the other at the perpendicular-linear polarization of applied pulses, or jointly at parallel-linear polarization. General equations are obtained for the amplitude of four-wave mixing signals with time resolution in these polarization configurations, which, in the limit of ultranarrow pulses, reduce to analytic functions of time and excitation and sample parameters. These equations are used to analyze signal characteristics in every polarization configuration. The results give a correct picture of biexciton effects and the polarization dependence of coherent four-wave mixing in GaAs quantum wells.
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.