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Journal of Russian Laser Research

Exciton-Boson Formalism in the Theory of Laser-Excited Semiconductors and Its Application in Coherent Four-Wave-Mixing Spectroscopy

Hoang Ngoc Cam

Published Sep 1, 2004• 1 citation
Publisher
DOI
10.1023/b:jorr.0000043731.28809.95

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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.
The exciton coherent signal decay rate in GaAs quantum wells, as measured in four-wave mixing experiments, depends on the polarization of the excitation pulses. Using polarization-dependent two-dimensional coherent spectroscopy, we show that this behavior is due to the bosonic character of excitons. Interference between two different quantum mechanical pathways results in a smaller decay rate for cocircular and colinear polarization of the optical excitation pulses. This interference does not exist for cross-linearly polarized excitation pulses resulting in a larger decay rate. Our result shows that the bosonic nature of excitons must be considered when interpreting ultrafast spectroscopic studies of exciton dephasing in semiconductors. This behavior should be considered while interpreting results of ultrafast spectroscopy experiments involving bosonlike excitations.
A detailed understanding of the population and coherence dynamics in optically driven individual emitters in solids and their signatures in ultrafast nonlinear-optical signals is of prime importance for their applications in future quantum and optical technologies. In a combined experimental and theoretical study on exciton complexes in single semiconductor quantum dots we reveal a detailed picture of the dynamics employing three-beam polarization-resolved four-wave mixing (FWM) micro-spectroscopy. The oscillatory dynamics of the FWM signals in the exciton-biexciton system is governed by the fine-structure splitting and the biexciton binding energy in an excellent quantitative agreement between measurement and analytical description. The analysis of the excitation conditions exhibits a dependence of the dynamics on the specific choice of polarization configuration, pulse areas and temporal ordering of driving fields. The interplay between the transitions in the four-level exciton system leads to rich evolution of coherence and population. Using two-dimensional FWM spectroscopy we elucidate the exciton-biexciton coupling and identify neutral and charged exciton complexes in a single quantum dot. Our investigations thus clearly reveal that FWM spectroscopy is a powerful tool to characterize spectral and dynamical properties of single quantum structures.